This article explains how to use a PS5 DualSense controller on PS4. Bluetooth Adapters, PS4, and DualSense The PS5 controller doesn't just work with the PS4, so you must pick up a Bluetooth adapter.

For example, you can take your controller which you use with your PS5, then seamlessly switch connection to a PC to play PC games, or connect it to a smartphone to enjoy Remote Play from your PS5.

The PS5 DualSense controller will soon get multi-device pairing, allowing seamless switching between your console, phone, PC, and more.

This will let you pair the DualSense controller with up to four devices simultaneously. So, for example, you have it paired to your PS5, PC, and mobile device that the same time.