Is the PS4 version still compatible with the PS5 console?

I've been trying to play the game but it feels like the PS5 console is lagging because I move the trigger and the movement of the operator takes like 1 second to actually get it. I factory reset the whole console and did the same with the controllers. I changed the DNS, cleaned the cache and the problem is still going. Is anybody else having this problem? Maybe the PS4 version is not working properly anymore on the PS5?

Any advice?