Hi, sadly I have no PS5 controller to test myself. AFAIK PS5 should work, but there is something you can try to do.
The game makes use of the SDL Controller Library. In the game's folder you should find a "gamecontrollerdb.txt", you can try and replace that with the newest version from the SDL_GameControllerDB GitHub Repo. Or you can even try to create a custom mapping following the instructions on that page.
Although I checked and PS5 controller should already be present in the version that's shipped with the game, so maybe you're having a completely different issue (what OS are you on?).
Hope this helps!