A Phase 2, Open-label, Multi-cohort Study to Assess the Efficacy and Safety of ASP5541 in Participants With Advanced 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 must have an estimated life expectancy of ≥ 12 months with mHSPC or ≥ 6 months with mCRPC. * Participant is able to understand and comply with all study requirements and procedures. * Participant has been diagnosed with mCRPC or mHSPC 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 is receiving ongoing ADT with a gonadotropin-releasing hormone (GnRH) analogue or has a history of bilateral orchiectomy (i.e., surgical or medical castration). Participant with mHSPC must have started castration therapy (medical or surgical) at least 14 days prior to Cycle 1 Day 1 (C1D1). Note: Participant who has not had a bilateral orchiectomy must have a plan to maintain effective GnRH analogue therapy for the duration of the study. * If the participant has mCRPC, participant has evidence of disease progression defined as 1 or more 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 progressive disease on CT/MRI per Response Evaluation Criteria in Solid Tumours (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 1 week 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. * If the participant has mCRPC, participant has a serum testosterone level \< 1.73 nmol/L (\< 50 ng/dL) at the Screening visit. * Male participant must agree to use contraception with female partner(s) of childbearing potential (including breastfeeding partner) throughout the treatment period and for 7 months after final ASP5541 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 administration. * Male participant must not donate sperm during the treatment period and for 7 months after final ASP5541 administration. * 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. Exclusion Criteria: * Participant has any concurrent disease, infection or comorbid condition that interferes with the ability of the subject to participate in the study, which places the subject at undue risk or complicates the interpretation of data. * Participant has known active central nervous system (CNS) metastases. Note: Participant with CNS metastases who has been treated with surgery and/or radiation therapy, who is off pharmacologic doses of glucocorticoids and who 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 the participant is currently in remission and has been in remission for ≥ 2 years * Any other cancer from which the participant has been disease-free for ≥5 years * 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. * QT interval corrected by Fridericia's formula (QTcF) ≥450 msec at Screening. If the QT interval corrected for heart rate intervals (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 New York Heart Association (NYHA) Class II or left ventricular ejection fraction measurement of \< 50% at baseline. * Cohorts 1 and 3: Participant 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. * Cohort 2: Participants must not have symptomatic heart failure, unstable or new-onset angina or myocardial infarction within the past 12 months. * Cohorts 1 and 3: Uncontrolled hypertension, defined as systolic blood pressure \> 160 mmHg or diastolic blood pressure \> 100 mmHg that has been confirmed by 2 successive measurements despite optimal medical management. * Cohort 2: 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. * Cohort 1 and 3: 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). * Cohort 2: Arterial thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks) within the last 12 months. * Participant has any unresolved National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) (version 5.0) Grade \> 2 toxicity at the Screening visit. Note: 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 30 days before screening, or has not 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 day 1. * Participant received a blood transfusion within 1 month of the first dose of study intervention. * 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% (if diabetes mellitus was previously diagnosed) or HbA1c \> 8% (if diabetes mellitus was previously undiagnosed). (Excluded participant 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 IgM positive, but testing for hepatitis A in screening is not required), hepatitis B (hepatitis B virus surface antigen positive, confirmed by hepatitis B virus DNA), or hepatitis C (hepatitis C virus antibody positive, confirmed by hepatitis C virus 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 (HIV antibody positive). * 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 criteria within 2 years before screening. * Participant received treatment with glucocorticoids greater than the equivalent of 10 mg per day of prednisone within 4 weeks prior to C1D1. The use of topical, intraocular, inhalational, intranasal or intra-articular glucocorticoids is permitted. * Participant received treatment with herbal medications with known anti-cancer properties or known effects on prostate physiology within 4 weeks prior to Cycle 1 Day 1 (e.g., saw palmetto, St. John's wort, turmeric/curcumin). Participants must agree not to use herbal products during study participation. * Participant is receiving current treatment with systemic ketoconazole, abiraterone acetate (AA) or any other cytochrome P450 17A1 (CYP17) inhibitor. Participant who has received systemic ketoconazole, AA or any other CYP17 inhibitor must have discontinued these agents ≥ 4 weeks prior to the first dose of study intervention. * Participant received prior systemic treatment with a strong inducer or inhibitor of cytochrome p450 3A4 (CYP3A4) within 4 weeks of first dose of study intervention. 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: Participant who switches from a high dose to a dose of 30 μg/day or less prior to first dose of study drug is eligible for study entry. * Participant is required to use any prohibited medication on the List of Excluded Concomitant Medications. * For mCRPC participants only: Participant has been treated with any of the following for prostate cancer, during the indicated time frame prior to enrollment: * Hormonal therapy (e.g., androgen receptor blockers \[AR\] antagonists, second-generation androgen receptor pathway inhibitors \[including enzalutamide, apalutamide, darolutamide, rezvilutamide and AA\], 5-alpha reductase inhibitors, estrogens, cyproterone acetate) within 4 weeks of C1D1. Note: Participant has been treated with bicalutamide within 6 weeks prior to enrollment is not permitted. Participant has been treated with all other GnRH analogues or antagonists is permitted. * Chemotherapy within 2 weeks or 5 half-lives of C1D1 (whichever is longer) * Biologic therapy within 4 weeks of C1D1 * Immunotherapy within 4 weeks of C1D1 * Radiation therapy (includes radioligands) within 4 weeks of C1D1 * For mHSPC participants only: 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 3 months prior to C1D1) with or without concurrent antiandrogens. * 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 weeks prior to C1D1. * Up to 6 cycles of docetaxel therapy, with the last dose of docetaxel ≤ 2 months prior to C1D1. A participant who has received docetaxel should have maintained a response to docetaxel of stable disease or better, by imaging and PSA, prior to C1D1. * Up to 6 months of ADT with GnRH agonists or antagonists or orchiectomy with or without concurrent antiandrogens prior to C1D1 if subject was treated with docetaxel, with no radiographic evidence of disease progression or rising PSA levels prior to C1D1. * Participant has received any investigational therapy within 4 weeks or 5 half-lives (whichever is longer) prior to C1D1. * Participant has received ASP5541 previously. * Participant has absolute neutrophil count \< 1500/μL, platelet count \< 100000/μL or 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: 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 \> 1.5 x upper limit of normal (ULN) (or \> 3 x ULN for participants with documented Gilbert's disease), or serum alanine aminotransferase or aspartate aminotransferase \> 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. * Participant has serum albumin \< 3.0 g/dL (30 g/L) at Screening. * Participant has a known or suspected hypersensitivity to ASP5541, prednisone, or any components of the formulations used. * Participant has a gastrointestinal disorder affecting absorption.