Study of Pembrolizumab (MK-3475) in Participants With Metastatic Castration-Resistant Prostate Cancer (mCRPC)(MK-3475-199/KEYNOTE-199)

Inclusion Criteria:

* Has histologically- or cytologically-confirmed adenocarcinoma of the prostate without small cell histology. Disease must be either metastatic or locally confined inoperable disease that cannot be treated with definitive intent (no chance for a curative intervention).
* Has supplied tumor tissue from a newly obtained biopsy or a biopsy obtained ≤12 months prior to study start and an archival specimen, if available, from a site not previously irradiated. Participants in Cohorts 1, 2, and 4 with visceral/measurable lesions must provide a newly obtained biopsy performed after the last line of systemic therapy or a biopsy obtained ≤12 months prior to study start and an archival specimen, if available. Participants in Cohorts 3 and 5 must at least provide an archival specimen.

For Cohorts 1, 2, and 3 only:

* Has been treated with:
* At least 1 targeted endocrine therapy (defined as second generation antiandrogen therapies that include but are not limited to abiraterone acetate with prednisone, enzalutamide, and next generation targeted agents such as ARN-509).
* At least 1 regimen/line of chemotherapy that contained docetaxel.
* No more than 2 chemotherapy regimens.
* No more than 3 regimens/lines of the aforementioned treatments (having failed/progressed on chemotherapy and targeted endocrine therapy).

For Cohorts 4 and 5 only:

* Failing or showing early signs of failure on current pre-chemotherapy enzalutamide treatment as defined by Prostate Cancer Working Group 3 (PCWG3) guidelines. Participants can have failed prior abiraterone treatment before current enzalutamide treatment. Participants must have had a clinically meaningful response to enzalutamide treatment. Enzalutamide must have been initiated no less than 4 weeks prior to the first dose of trial treatment and be continued throughout the study.

For All Cohorts:

* Has documented prostate cancer progression within 6 months prior to screening, as determined by the Investigator, by means of one of the following: 1) PSA progression as defined by a minimum of 3 rising PSA levels with an interval of ≥1 week between each assessment where the PSA value at screening should be ≥2 ng/mL, OR, 2) Radiographic disease progression in soft tissue or bone with or without PSA progression
* Has ongoing androgen deprivation with total serum testosterone \<50 ng/dL (\<2.0 nM).
* Participants receiving bone resorptive therapy (including but not limited to bisphosphonate or Receptor activator of nuclear factor kappa-B ligand \[RANK-L inhibitor\]) must have been on stable doses for ≥4 weeks prior to first dose of study drug.
* Has a performance status of 0, 1 or 2 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale
* Participants of reproductive potential must agree to use an adequate method of contraception, starting with the first dose of study drug through at least the time needed to eliminate each study intervention after the last dose of study intervention. The length of time required to continue contraception after the last dose of enzalutamide is 30 days.
* Demonstrates adequate organ function.

Exclusion Criteria:

For All Cohorts:

* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigation device within 4 weeks of the first dose of study drug.
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.
* Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to the first dose of study drug or who has not recovered (i.e., ≤ Grade 1 or at Baseline) from AEs due to mAbs administered more than 4 weeks earlier.
* Has had prior chemotherapy, targeted small molecule therapy, or external beam radiation therapy within 4 weeks prior to the first dose of study drug or who has not recovered (i.e., ≤ Grade 1 or at Baseline) from AEs due to a previously administered agent.
* Has a known additional malignancy that has had progression or has required active treatment in the last 3 years. Exceptions include basal cell carcinoma of the skin and squamous cell carcinoma of the skin that has undergone potentially curative therapy.
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis.
* Has an active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs).
* Has evidence of interstitial lung disease and/or a history of (non-infectious) pneumonitis that required steroids, or current pneumonitis.
* Has an active infection requiring systemic therapy.
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
* Has previously participated in any other pembrolizumab (MK-3475) trial, or received prior therapy with an anti-programmed cell death 1 (anti-PD-1, anti-PD ligand 1 \[anti-PD-L1\], and anti-PD-L2 \[including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways\]).
* Has a known history of Human Immunodeficiency Virus (HIV).
* Has known active Hepatitis B or Hepatitis C.
* Has received a live vaccine within 30 days of planned start of study drug. Any licensed coronavirus disease 2019 (COVID-19) vaccine (including for Emergency use) in a particular country is allowed in the study as long as they are messenger ribonucleic acid (mRNA) vaccines, adenoviral vaccines, or inactivated vaccines. Investigational vaccines (ie, those not licensed or approved for Emergency Use) are not allowed.

For Cohorts 4 and 5 only:

* Has received prior chemotherapy (e.g., docetaxel) for mCPRC.
* Has any condition (cardiac, neurologic, absorption) other than clinically failing or showing early signs of failure on enzalutamide treatment that would require imminent discontinuation of enzalutamide treatment.