Study of AZD5305 When Given in Combination With New Hormonal Agents in Patients With Metastatic Prostate Cancer

Inclusion Criteria: For whole study: * Age ≥ 18 at the time of screening. * Histologically confirmed diagnosis of metastatic prostate cancer. * Candidate for treatment with enzalutamide, abiraterone acetate, darolutamide or apalutamide with documented current evidence of metastatic prostate cancer. * Surgically or medically castrated. * Adequate organ and marrow function. * Eastern Cooperative Oncology Group Performance Status (ECOG PS): 0-1 with no deterioration over the previous 2 weeks. * Life expectancy ≥ 16 weeks. * Non-sterilized male patients who are sexually active with a female partner of childbearing potential must use a condom with spermicide from screening to approximately 6 months after the last dose of study treatment . For Patients Recruited Specifically to tumour Pharmacodynamic Cohorts: • Patients must have at least 1 tumour suitable for paired biopsies For Part A: • Patients with Metastatic Castrate ion-Resistant Prostate Cancer (mCRPC) or Metastatic Castration Sensitive Prostate Cancer (mCSPC). For Part B: • Patients must have mCSPC (de novo or recurrent) with a baseline PSA value of ≥ 0.2 ng/mL Exclusion Criteria: For Part A mCRPC patients only: * Any previous treatment with a new hormonal agent (NHA), poly (adenosine diphosphateribose) polymerase inhibitor (PARPi), Lutetium prostate-specific membrane antigen (Lu-PSMA), platinum chemotherapy * Patients recruited to the PDc cohorts should not have received a prior use of new hormonal agents (NHA). For Part A and Part B mCSPC Patients: * Any previous treatment with a PARPi, platinum, NHA, Immuno-oncology (IO), radiopharmaceutical therapy, or prior treatment with docetaxel in mCSPC setting. * Concomitant use of medications or herbal supplements known to be: 1. Strong and moderate CYP3A4 inducers/inhibitors (applies for all arms) 2. For Arm 1 (enzalutamide) patients: Strong CYP2C8 inhibitors 3. For Arm 3 (darolutamide) patients: Strong P-glycoprotein inducers * Concomitant use of drugs that are known to prolong or shorten QT and have a known risk of Torsades de Pointes. * Treatment with any of the following: 1. Any investigational agents or study interventions from a previous clinical study within 5 half lives or 3 weeks (whichever is longer) of the first dose of study treatment. 2. Any other anticancer treatment within the following time periods prior to the first dose of study treatment: (i) Cytotoxic and non-cytotoxic treatment: 3 weeks or 5 half-lives (whichever is shorter). (ii) Biological products including immuno-oncology agents: 4 weeks before enrolment. 3. Any live virus or bacterial vaccine within 28 days of the first dose of study treatment. * Any concurrent anticancer therapy or concurrent use of prohibited medications. * Major surgery within 4 weeks prior to the first dose of study treatment. * Radiotherapy with a wide field of radiation within 4 weeks or radiotherapy with a limited field of radiation for palliation within 2 weeks of the first dose of study treatment. * With the exception of alopecia, and peripheral neuropathy; any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 at the time of study enrolment. * Any history of persisting (\> 2 weeks) severe pancytopenia. * Spinal cord compression, or brain metastases unless asymptomatic and treated and stable. * Any evidence of severe or uncontrolled systemic diseases, including, active bleeding diatheses, or active infection including hepatitis B, hepatitis C and human immunodeficiency virus (HIV). * Patients with any known predisposition to bleeding (eg, active peptic ulceration, recent \[within 6 months\] haemorrhagic stroke, proliferative diabetic retinopathy. * Any clinically significant cardiac disorders including QT prolongation, abnormal electrocardiogram (ECG). * Any clinically significant cardiovascular diseases including symptomatic heart failure, uncontrolled hypertension, acute coronary syndrome, cardiomyopathy, valvular heart disease, atrial fibrillation, stroke. * Patients with history of myelodysplastic syndrome (MDS)/ acute myeloid leukaemia (AML). * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection. * Known allergy or hypersensitivity to investigational product(s) or any of the excipients of the investigational product(s). * Any condition that would interfere with evaluation of the study treatment or interpretation of patient safety or study results. * Uncontrolled intercurrent illness within the last 12 months, including but not limited to, active interstitial lung disease, serious chronic gastrointestinal (GI) conditions associated with diarrhoea, or psychiatric illness/social situations * History of another primary malignancy except for malignancy treated with curative intent with no known active disease within 3 years before the first dose of study treatment and of low potential risk for recurrence. * Concurrent enrolment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study. * Arm 1 (Enzalutamide) and Arm 4 (Apalutamide): History of seizure or any condition that may predispose to seizure (eg, prior cortical stroke, significant brain trauma). * Arm 2 (Abiraterone acetate) only: (i) Active infection or other medical condition that would contraindicate the use of systemic steroids (prednisone/prednisolone). (ii) Low serum potassium (\< 3.5 mmol/L). (iii) History of uncontrolled pituitary or adrenal dysfunction. * Arm 4 (Apalutamide): (i) Moderate or severe skin conditions or diseases that could affect the skin (eg. scleroderma, lupus). (ii) Any skin or medical condition that in the Investigator's opinion could increase the risk of skin toxicity.