The PS5 controller doesn't just work with the PS4, so you must pick up a Bluetooth adapter. This will usually come in the form of a USB device which needs to be plugged into the PS4.

News Obsidian Entertainment Pentiment Pentiment Update 1.3 PS4 PS5 Pentiment Update 1.3 Patch Notes Reveal High Contrast Fix, PS5 & PS4 Controller Graphics Update Michael Harradence / March 13, 2024 ...

Controller cross-compatibility is always a discussion when a new console releases, so it was inevitable that players would start looking for some way to use the DualSense on the PS4.