Participants with mCRPC previously treated with docetaxel-based chemotherapy in Cohorts 1 to 3 will receive monotherapy with pembrolizumab. Chemotherapy-naïve subjects with mCRPC either having failed or showing signs of failure with enzalutamide in Cohorts 4 and 5 will receive pembrolizumab monotherapy in addition to their current regimen of enzalutamide. In all cohorts, pembrolizumab administration will occur on Day 1 of each 3-week dosing cycle and will continue for a maximum of 35 cycles (approximately 2 years) unless specific withdrawal/discontinuation criteria are met. Participants who discontinue after 35 infusions of pembrolizumab for reasons other than disease progression or intolerability, or who discontinue after attaining a complete response may be eligible for up to 17 additional infusions (approximately 1 year) after they have experienced disease progression.