Even though the PlayStation 5 DualSense controller is not usually compatible with the PS4, there are a couple of workarounds you can use to get it to work.

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. The adapter then ...

First of all, ensure the light bar on top of the controller isn’t on. If this is the case, hold down the PS button on the centre of the controller until it turns off. Head to Settings > Accessories > ...