A Study to Evaluate the Safety and Drug Levels of ASP5541 in Chinese 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 Eastern Cooperative Oncology Group (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 metastatic hormone-sensitive prostate cancer (mHSPC) or ≥ 6 months with metastatic castration-resistant prostate cancer (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 androgen deprivation therapy (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 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. 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. 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. * 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. * 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 the start of study medication). * 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 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