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

Hormone therapy, or androgen deprivation therapy (ADT) is a standard way to treat prostate cancer. It works by reducing the amount of the main male sex hormone, testosterone in the body. Androgen receptor pathway inhibitors (ARPIs) are another type of hormone therapy. They either slow down how much testosterone is made or block testosterone from reaching the prostate cancer cells. Abiraterone acetate (AA) is an ARPI that is used to treat advanced prostate cancer. This type of treatment is usually given as a tablet with a steroid called prednisone/prednisolone to manage any medical problems from the hormone therapy. ASP5541 is a different form of abiraterone acetate. It is given as an injection into the muscle. In this study, ASP5541 will be given to men with advanced prostate cancer, both with and without prednisone/prednisolone. This study will check the safety of ASP5541 and compare how well ASP5541 works in men with advanced prostate cancer compared to abiraterone acetate. The main aims of the study are: * To check how well ASP5541 with prednisone/prednisolone works compared to AA with prednisone/prednisolone in men with advanced prostate cancer who haven't previously been treated with an ARPI. * To check the safety of ASP5541 given by itself in men with advanced prostate cancer that haven't previously been treated with an ARPI. * To check how well ASP5541 given by itself works compared to AA with prednisone/prednisolone in men with advanced prostate cancer that haven't previously been treated with an ARPI. * To check the safety of ASP5541 with prednisone/prednisolone in Japanese men with advanced prostate cancer. Adult men with a certain type of advanced prostate cancer can take part. Their cancer has spread to other parts of the body (metastatic). The different types are: * Metastatic hormone-sensitive prostate cancer (mHSPC). Prostate cancer that needs testosterone to grow. * Metastatic castration-resistant prostate cancer (mCRPC). Prostate cancer that continues to grow even when testosterone levels are low. In this study there will be 3 treatment groups: * In Group 1, men with mCRPC who haven't previously been treated with an androgen receptor pathway inhibitor will either be given ASP5541 and prednisone/prednisolone or be given abiraterone acetate and prednisone/prednisolone. * In Group 2, men with mHSPC who haven't previously been treated with an androgen receptor pathway inhibitor will either be given ASP5541 by itself or be given abiraterone acetate with prednisone/prednisolone. * In Group 3, Japanese men with mCRPC or mHSPC who may or may not have previously been treated with an androgen receptor pathway inhibitor will be given ASP5541 with prednisone/prednisolone. ASP5541 will be given as an injection into a muscle every 12 weeks. Men with mCRPC will take prednisone/prednisolone twice daily and men with mHSPC will take prednisone/prednisolone once daily. Abiraterone acetate will be given as tablets to be taken once daily. All groups will also receive the standard of care treatment, such as androgen deprivation therapy. The men in the study will visit their clinic regularly during and after treatment for health checks, including checking for any medical problems. Some men (Group 2) will check their blood pressure weekly at home. On some visits they will also have scans to check for any changes in their cancer. The number of visits and type of safety checks done at each visit will depend on the health of each person and when they completed their treatment.