You should be able to play ps4 games on the ps5 just fine with a ps4 controller plugged into the xim. You can’t play ps5 games with a ps4 controller plugged in, because of backwards compatibility issues. If you want to play ps5 games with a xim, then you need to plug in a 3rd party controller. I think the cheapest 3rd party controller is the hori mini gamepad for like $30 USD. https://www.amazon.com/Mini-Wired-Gamepad-HORI-playstation-4/dp/B01A6MKVAA
The Hori Mini Wired Gamepad. $29.99.