No, PS5 does not allow third party Bluetooth products to connect natively to the PlayStation 5 console. Instead, they have their own proprietary wireless signal for their devices and consoles. As a result, if you want to connect your third-party Bluetooth headsets, you'll need a Bluetooth adapter/Bluetooth signal transmitter/or a USB C dongle for Bluetooth. That should enable your headset to pair with it, and in turn be used for sound on PS5.