A Phase 2 Study to Evaluate the Effects of ASP5541 in Participants With Prostate Cancer

Inclusion Criteria: * Participant is diagnosed with histologically or cytologically confirmed adenocarcinoma of the prostate without neuroendocrine differentiation or small cell features. * Participant has ECOG performance status of 0 or 1, or ECOG performance status of 2 if due to bone pain. * Participant with mHSPC must have an estimated life expectancy of ≥ 12 months or \> 6 months if participant has mCRPC. * Participant is able to understand and comply with all study requirements and procedures, including completion of PRO questionnaires. * Male participant must agree to use defined forms of contraception with female partner(s) of childbearing potential (including breastfeeding partner) throughout the treatment period and for 7 months after final ASP5541 or for 3 months after AA study intervention administration. * Male participant must agree to remain abstinent or use a condom with pregnant partner(s) for the duration of the pregnancy throughout the investigational period and for 7 months after final ASP5541 or for 3 months after AA study intervention administration. * Male participant must not donate sperm during the treatment period and for 7 months after final ASP5541 or for 3 months after AA study intervention administration. * Participant has adequate ventrogluteal muscle mass for an intramuscular injection. * Participant agrees not to participate in another interventional study while receiving ASP5541 in the present study. * Participant should have normal serum potassium (within the local laboratory normal range) at screening without supplementation. Inclusion Criteria for Cohort 1 * Participant has been diagnosed with mCRPC documented by metastatic lesions on a bone scan, computed tomography (CT), magnetic resonance imaging (MRI) or prostate-specific membrane antigen positron emission tomography (PSMA-PET). * Participant has evidence of disease progression defined as at least 1 of the following criteria at study entry. * Evidence of radiographic progression of disease prior to first dose and following the most recent prostate cancer treatment defined as PD on CT/MRI per RECIST v1.1 or on a bone scan per PCWG3. * PSA progression defined as an increase in PSA of at least 25% and ≥ 1 ng/mL above the nadir, confirmed by a second value at least 1 wk later, and with at least 1 of the measurements within 90 days prior to screening. PSA nadir is defined as the lowest PSA during or after the most recent treatment. * Participant is receiving ongoing ADT with a gonadotropin-releasing hormone (GnRH) analogue or has a history of bilateral orchiectomy (i.e., surgical or medical castration). NOTE: Participants who have not had a bilateral orchiectomy must have a plan to maintain effective GnRH analogue therapy for the duration of the study. * Participant has a serum testosterone level \< 1.73 nmol/L (\< 50 ng/dL) at Screening visit. * Participant is able to swallow AA. Inclusion Criteria for Cohort 2 * Participant has been diagnosed with mHSPC documented by metastatic lesions on a bone scan, CT, MRI or PSMA-PET. * Participant must have started castration therapy (i.e., medical or surgical) at least 14 days prior to Cycle 1 Day 1. NOTE: A participant who has not had a bilateral orchiectomy must have a plan to maintain effective GnRH analogue therapy for the duration of the study. * Participant should have a baseline morning serum cortisol of ≥ 14 mcg/dL. * Participant is able to swallow AA. * For Groups B and C, participant has accessible archival tumor tissue from the primary tumor (preferred) or metastatic site (excluding bone) for which source and availability have been confirmed prior to study treatment. Exclusion Criteria: * Participant has any concurrent disease, infection or comorbid condition that interferes with the ability of the participant to participate in the study, which places the participant at undue risk or complicates the interpretation of data. * Participant has known active central nervous system (CNS) metastases. NOTE: a participant with CNS metastases that have been treated with surgery and/or radiation therapy, who is no longer taking pharmacologic doses of glucocorticoids and is neurologically stable, is eligible. * Participant has a known additional malignancy beyond prostate cancer that requires active treatment, with the exception of any of the following: * Adequately treated basal cell carcinoma, squamous cell carcinoma of the skin or in situ carcinoma of any type * Adequately treated Stage I cancer from which participant is currently in remission and has been in remission for ≥ 2 years * Any other cancer from which participant has been disease-free for ≥ 5 years * Participant has any unresolved National Cancer Institute - Common Terminology Criteria for Adverse Events (NCI-CTCAE) (v5.0) Grade \> 2 toxicity at the Screening visit. NOTE: A participant receiving ongoing hormone replacement therapy for endocrine immune-related AEs without clinical symptoms will not be excluded. * Participant has had major surgery (e.g., requiring general anesthesia) within 90 days before screening, or will not have fully recovered from surgery, or has major surgery planned during the time the participant is expected to participate in the study. * Participant has/had febrile illness or symptomatic, viral, bacterial (including upper respiratory infection) or fungal (noncutaneous) infection within 28 days prior to Cycle 1 Day 1. * Participant received a blood transfusion within 1 month of Cycle 1 Day 1. * Participant has a history of impaired pituitary or adrenal gland function (e.g., Addison's disease, Cushing's syndrome). * Participant has hemoglobin A1c (HbA1c) \> 10% and was previously diagnosed with diabetes mellitus. Participant has HbA1c \> 8% and was not previously diagnosed with diabetes mellitus (excluded participants may be rescreened after referral and evidence of improved control of their condition). * Participant has jaundice or known current active liver disease from any cause, including hepatitis A (hepatitis A virus immunoglobulin M (IgM) positive, but testing for hepatitis A in screening is not required), hepatitis B \[hepatitis B surface antigen (HBsAg) positive, or hepatitis B virus (HBV) DNA positive if HBsAg negative/anti-HBc positive\]), or hepatitis C virus (HCV) antibody positive, confirmed by HCV RNA). * Participant has moderate or severe hepatic impairment (Child-Pugh Class B or C). * Participant has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by a local health authority. * Participant has a body mass index \> 40 kg/m2. * Participant has a history of drug or alcohol abuse according to Diagnostic and Statistical Manual of Mental Disorders, 5th edition (DSM-5) criteria within 2 yrs before screening. * Participant has received treatment with glucocorticoids greater than the equivalent of 10 mg per day of prednisone within 4 wks prior to Cycle 1 Day 1. The use of topical, intraocular, inhalational, intranasal or intra-articular glucocorticoids is permitted. * Participant received treatment with herbal medications within 4 wks prior to Cycle 1 Day 1 (e.g., saw palmetto). Participants must agree not to use herbal products during study participation. * Participant is receiving current treatment with systemic ketoconazole or any other cytochrome 450 (CYP17) inhibitor. Participants who have received systemic ketoconazole or any other CYP17 inhibitor must have discontinued these agents ≥ 4 wks prior to Cycle 1 Day 1. * Participant is receiving CYP2D6 substrates with a narrow therapeutic index (applies to Cohorts 1 \& 2 only). * Participant received prior systemic treatment with a strong inducer or inhibitor of CYP3A4 within 4 weeks of Cycle 1 Day 1. Concomitant use of strong inducers or inhibitors of CYP3A4 are not permitted on study. * Participant requires use of biotin (i.e., vitamin B7) or supplements containing biotin higher than the daily adequate intake of 30 µg. NOTE: Participants who switch from a high dose to a dose of 30 µg/day or less prior to Cycle 1 Day 1 are eligible for study entry. * Participant has received a live, attenuated vaccine within 30 days of planned start of study therapy. Examples of live, attenuated vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette Guérin and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live, attenuated vaccines and are not allowed. * Participant is required to use any prohibited medication per List of Excluded Concomitant Medications. * Participant has received any investigational therapy within 4 weeks (wks0 or 5 half-lives (whichever is longer) prior to Cycle 1 Day 1. * Participant has received ASP5541 (PRL-02) previously. * Participant has absolute neutrophil count \< 1500/μL, platelet count \< 100,000/μL, hemoglobin \< 9 g/dL (6.2 mmol/L ) or international normalized ratio (INR) ≥ 1.5 (unless participant is taking oral anticoagulants, in which case INR ≤ 2.0 is permitted) at Screening. NOTE: A participant may not have received any growth factors within 7 days or blood transfusions within 28 days prior to the hematology values obtained at Screening. * Participant has serum total bilirubin (TBL) \> 1.5 x upper limit of normal (ULN) (except participants with documented Gilbert's disease) or serum alanine aminotransferase (ALT) or aspartate aminotransferase (AST) \> 2.5 x ULN at Screening. * Participant does not have adequate renal function defined as a calculated creatinine clearance \< 30 mL/min as determined by a validated algorithm for calculating creatinine clearance at Screening. * Participant has serum albumin \< 3.0 g/dL (30 g/L) at Screening. * Participant has a known or suspected hypersensitivity to ASP5541, AA (Cohorts 1 and 2 only), prednisone or any components of the formulations used in the study. * Participant has a gastrointestinal (GI) disorder affecting absorption. Exclusion Criteria for Cohort 1 * Prior treatment with a second-generation ARPI (e.g., AA, enzalutamide, apalutamide or darolutamide). NOTE: limited treatment with a second-generation ARPI in the neo-adjuvant, adjuvant or non-metastatic biochemically recurrent setting is permitted as long as there was no evidence of disease progression for at least 6 months following last dose. * Treatment with any of the following for prostate cancer, during the indicated timeframe prior to enrollment: * Hormonal therapy (e.g., AR antagonists, 5 alpha reductase inhibitors, estrogens, cyproterone acetate) within 4 wks of Cycle 1 Day 1. Note: Treatment with bicalutamide within 6 wks prior to enrollment is not permitted. Treatment with GnRH agonists or antagonists is permitted. * Chemotherapy within 2 wks or 5 half-lives of Cycle 1 Day 1 (whichever is longer) * Biologic therapy within 4 wks of Cycle 1 Day 1 * Immunotherapy within 4 wks of Cycle 1 Day 1 * Radiation therapy (includes radioligands) within 4 wks of Cycle 1 Day 1 * Participant with a known BRCA mutation should be excluded unless they have previously received a PARPi or are not eligible for a PARPi, or a PARPi is not available. * Participant has clinically significant cardiac disease, defined as any of the following: * Clinically significant cardiac arrhythmias including bradyarrhythmia, which are poorly controlled. Rate-controlled atrial fibrillation is permitted. * Congenital long QT syndrome. * QTcF ≥ 450 msec at Screening. If the QTc is prolonged in a participant with a pacemaker or bundle branch block, the participant may be enrolled in the study if confirmed by the medical monitor. * History of clinically significant cardiac disease or congestive heart failure greater than NYHA Class II or left ventricular ejection fraction measurement of \< 50% at baseline. Participants must not have unstable angina (symptoms at rest) or new-onset angina within the last 3 months or myocardial infarction within the past 6 months. * Uncontrolled hypertension, defined as systolic BP \> 160 mmHg or diastolic BP\> 100 mmHg that has been confirmed by 2 successive measurements despite optimal medical management. * Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within the 3 months before start of study medication (except for adequately treated catheter-related venous thrombosis occurring \> 1 month before Cycle 1 Day 1). Exclusion Criteria for Cohort 2 * Prior treatment with a second-generation ARPI (e.g., AA, enzalutamide, apalutamide or darolutamide). Note: limited treatment with a second-generation ARPI in the neo-adjuvant, adjuvant or non-metastatic biochemically recurrent setting is permitted as long as there was no evidence of disease progression for at least 6 months following last dose. * Participant has received any prior pharmacotherapy, radiation therapy or surgery for metastatic prostate cancer. The following exceptions are permitted: * Up to 4 months of ADT with GnRH agonists or antagonists or orchiectomy (within 4 months prior to Cycle 1 Day 1) with or without concurrent antiandrogens, with no radiographic evidence of disease progression or rising PSA levels prior to Cycle 1 Day 1. * Participant may have 1 course of palliative radiation or surgical therapy to treat symptoms resulting from metastatic disease if it was administered at least 4 wks prior to Cycle 1 Day 1. Radiotherapy to the prostate for participants with low volume metastatic disease is also permitted if it was administered at least 4 wks prior to Cycle 1 Day 1. * Up to 6 cycles of docetaxel therapy, with the last dose of docetaxel ≤ 2 months prior to Cycle 1 Day 1. A participant who has received docetaxel should have maintained a response to docetaxel of stable disease or better, by imaging and PSA, prior to Cycle 1 Day 1. * Up to 6 months of ADT with GnRH agonists or antagonists or orchiectomy with or without concurrent antiandrogens prior to Cycle 1 Day 1 if participant was treated with docetaxel, with no radiographic evidence of disease progression or rising PSA levels prior to Cycle 1 Day 1. * Participant has clinically significant cardiac disease, defined as any of the following: * Clinically significant cardiac arrhythmias including bradyarrhythmia, which are poorly controlled. Rate-controlled atrial fibrillation is permitted. * Congenital long QT syndrome. * QTcF ≥ 450 msec at Screening. If the QTc is prolonged in a participant with a pacemaker or bundle branch block, the participant may be enrolled in the study if confirmed by the medical monitor. * History of clinically significant cardiac disease or congestive heart failure greater than NYHA Class II or left ventricular ejection fraction measurement of \< 50% at baseline. Participants must not have symptomatic heart failure, unstable or new-onset angina or myocardial infarction within the past 12 months. * Uncontrolled hypertension, defined as systolic BP \> 140 mmHg or diastolic BP \> 90 mmHg that has been confirmed by 2 successive measurements despite optimal medical management. Participants may be receiving a maximum of 2 antihypertensives that were initiated at least 3 months prior to Cycle 1 Day 1. * Arterial thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks) within the last 12 months. * Venous thromboembolic events (deep vein thrombosis or pulmonary embolism) within the 3 months before start of study medication (except for adequately treated catheter-related venous thrombosis occurring \> 1 month before Cycle 1 Day 1).