Sony has stated that the dual sense controller is not compatible with ps4 when they are connected to each other by Bluetooth. So, can a ps5 controller work on a ps4 the answer is simple no as the reason is stated above. But there are a few ways you can use both together indirectly. For connected both you will require a ps remote play or titan two adapter. Once you enable the remote play now you can use both them on Mac or your desktop.