Multiple Ascending Dose Study of MK-5160 in Participants With Type 1 and Type 2 Diabetes Mellitus (MK-5160-002)

Inclusion Criteria: * For Part 1 (T1DM): * Be male, or female of non-childbearing potential. A female of non-childbearing potential defined as a female who is postmenopausal without menses for at least 1 year and has a follicle stimulating hormone (FSH) value in the postmenopausal range upon pretrial (screening) evaluation OR a female who is status post hysterectomy, oophorectomy or tubal ligation. * Be judged to be in good health * Have a diagnosis of T1DM as defined by standard diagnostic criteria for ≥12 months at time study participation * Be on stable doses of basal insulin over the 2-week period prior to screening and over the 2 weeks prior to dosing. * Have a total daily insulin requirement (basal plus prandial) of ≤ 1.2 units/kg. * Have a hemoglobin A1C (HbA1c) ≤10% at the time of study participation. * Have a Body Mass Index (BMI) ≥18.5 kg/m\^2 and ≤ 32 kg/m\^2. BMI = mass (kg)/height (m)\^2 * Be a non-smoker or smoker who uses no more than 5 cigarettes or equivalent (e.g., e-cigarettes) per day over the prior 3 month period also may be enrolled (at the discretion of the investigator). The subject must agree to follow the smoking restrictions defined by the clinical research unit (CRU). * For Part 2 (T2DM): * Be male, or female of non-childbearing potential. A female of non-childbearing potential defined as a female who is postmenopausal without menses for at least 1 year and has a FSH value in the postmenopausal range upon pretrial (screening) evaluation OR a female who is status post hysterectomy, oophorectomy or tubal ligation. * Be judged to be in good health * Have a diagnosis of T2DM as defined by standard diagnostic criteria for ≥12 month at time of study participation. * T2DM participants are not required to have been on insulin. If on insulin, participants should have a total daily insulin requirement of ≤ 1.2 units/kg, and have been on stable doses of basal insulin over the 2-week period prior to screening and over the 2 weeks prior to dosing. * Meet one of the following criteria: 1. Be on no anti-hyperglycemic agent (AHA), or on metformin monotherapy or metformin plus a dipeptidyl peptidase-4 (DPP4) inhibitor at stable doses for at least 8 weeks prior to screening, with a screening HbA1C ≥7.0 and ≤10.0%. 2. Be on either a sulfonylurea (e.g. glyburide) or an alpha-glucosidase inhibitors (e.g., acarbose) alone or in combination with metformin at stable doses for at least 8 weeks prior to screening with a screening HbA1C ≥7.0 and ≤9.0%. Participants on these medications must be willing to stop the sulfonylurea or alpha-glucosidase inhibitor after screening once they qualify for study participation. * Have a BMI ≥18.5 kg/m\^2 and ≤ 35.0 kg/m\^2 BMI = mass (kg)/height (m)\^2 * May be on selected standard medications for T2DM, including alpha-glucosidase inhibitors (e.g., acarbose), sulfonylureas (e.g. glyburide), DPP-4 inhibitors, and metformin. Participants on alpha-glucosidase inhibitors and/or sulfonylureas must stop these medications for at least one week prior to checking into the site and for the duration of the trial through the last dose of MK-5160/glargine. Participants on metformin or DPP-4 inhibitors may continue on their home dose for the duration of the trial. Participants on SGLT2 inhibitors (gliflozins), thiazolidinediones or GLP-1 agonists are excluded. * Be a nonsmoker or smoker who uses no greater than 5 cigarettes or equivalent (e.g., e-cigarettes) daily over the prior 3 month period. Participants must agree to follow the smoking restrictions defined by the CRU. Exclusion Criteria: * For Part 1 (T1DM) and Part 2 (T2DM): * Is under the age of legal consent * Is mentally or legally incapacitated, has significant emotional problems at the time of pretrial (screening) visit or expected during the conduct of the trial or has a history of clinically significant psychiatric disorder of the last 5 years. Participants who have had situational depression may be enrolled in the trial at the discretion of the investigator. * Has a history of clinically significant endocrine (excluding diabetes mellitus), gastrointestinal, cardiovascular, hematological, hepatic, immunological, renal, respiratory, genitourinary or major neurological (including stroke and chronic seizures) abnormalities or diseases. Participants with a history of uncomplicated kidney stones, as defined as spontaneous passage and no recurrence in the last 5 years, or childhood asthma may be enrolled in the trial at the discretion of the investigator. * Has a history of cancer (malignancy) Exceptions: (1) Participants with adequately treated non-melanomatous skin carcinoma or carcinoma in situ of the cervix may participate in the trial; (2) Participants with other malignancies which have been successfully treated ≥10 years prior to the pretrial visit * Has a history of significant multiple and/or severe allergies (e.g. food, drug, latex allergy), or has had an anaphylactic reaction or significant intolerability (i.e. systemic allergic reaction) to prescription or non-prescription drugs or food. * Is positive for hepatitis B surface antigen, hepatitis C antibodies or HIV at Screening. * Had major surgery, donated or lost 1 unit of blood (approximately 500 mL) within 4 weeks prior to the pretrial visit. * Has participated in another investigational trial within 4 weeks (or 5 half-lives), whichever is greater, prior to the pretrial visit. * Is unable to refrain from or anticipates the use of any medication, including prescription and non-prescription drugs or herbal remedies beginning approximately 2 weeks (or 5 half-lives) prior to administration of the initial dose of trial drug, throughout the trial (including washout intervals between treatment periods), until the post-trial visit. Certain medications, such as antihypertensives and aspirin, are permitted. * Consumes greater than 3 glasses of alcoholic beverages (1 glass is approximately equivalent to: beer \[354 mL/12 ounces\], wine \[118 mL/4 ounces\], or distilled spirits \[29.5 mL/1 ounce\]) per day. * Consumes excessive amounts, defined as greater than 6 servings (1 serving is approximately equivalent to 120 mg of caffeine) of coffee, tea, cola, energy-drinks, or other caffeinated beverages per day. * Is a regular user of cannabis or any illicit drugs, or has a history of drug (including alcohol) abuse within approximately 6 months. * Has the diagnosis of hypoglycemia unawareness, or has had one or more severe hypoglycemic episodes associated with hypoglycemic seizures, comas or unconsciousness within 6 months prior to dosing. * Has used systemic (intravenous, oral, inhaled) glucocorticoids within 3 months of screening or is anticipated to require treatment with systemic glucocorticoids during study participation. * Has other major medical problems requiring medication (i.e., history of myocardial infarction, hypercholesterolemia). Participants on aspirin as prophylaxis may be enrolled, provided there is no history of MI or other thromboembolic event, or a history of coronary atherosclerosis. * Has a known history of celiac disease or significant food allergy, at the discretion of the Investigator and Sponsor. * Has a history of hypersensitivity to pharmacologic insulins or to any of the inactive ingredients in regular human insulin, or to any E.coli-derived drug product. * For Part 1 (T1DM) Only: * Has a history of diabetic ketoacidosis in the last 12 months. * For Part 2 (T2DM) Only * Has been treated with a sodium/glucose cotransporter 2 (SGLT2) inhibitor (gliflozins), thiazolidinedione or Glucagon-like peptide-1 (GLP-1) receptor agonist within the past three months.