This article explains how to connect AirPods to a PS5, including what you'll need to do to connect them. While this article specifically covers connecting AirPods to a PS5, these instructions will work for any Bluetooth headset (or device).
To connect AirPods to PS5, follow these steps:
Make sure your AirPods are charged. If your Bluetooth adapter plugs into the PS5 controller and therefore uses a battery, make sure that's charged as well. Adapters that plug into the PS5 or TV draw power from those devices and don't need to be charged.
Connect the Bluetooth adapter to your PS5, TV, or controller.