Finishes: Colors & Stains

Go to the game hub for the PS4 game. Select the upgrade offer on the game hub and review the upgrade offer. Select Download (or purchase with the discount price) to download/purchase content. After the download is complete, you can play the PS5 digital game by inserting the PS4 game disc.

Yes, Call of Duty: Black Ops Cold War is cross-play, cross-progression, and cross-generation enabled. Once you upgrade from the current generation console to the next generation console, your profile, progression, and stats will move with you.