Call of Duty: Black Ops Cold War players on PS5 may be launching the PS4 version
Make sure your not downgrading your upgrade
As reported, the mistake can occur if you pick the Ultimate Edition or Cross-gen bundles of the game on PS5. Both come with the PS5 and PS4 versions of Call of Duty: Black Ops Cold War, and if you download them all at once, there's a chance you could be booting up the PS4 version when you get stuck into the game.
Activision Support addressed how to make sure you're playing the next-gen version of the FPS from Treyarch and Raven Software. By going to the game tile on your PS5 dashboard, you then need to scroll down and highlight the "Play" tab. There you should see three dots you can click on to open up the menu. From here, you'll be able to select "PS5 Full Call of Duty: Black Ops Cold War", which will then launch the next-gen version of the game.
There are some reports that this situation is providing another problem for PS5 users. While you're able to delete the PS4 version from your PS5 if you don't want to play that version , it seems there is some sort of download queue bug preventing people from downloading the PS5 version if they have the PS4 version only installed on their PS5. Reports indicate a factory reset sorts this out, but it's certainly not an ideal situation.