How to connect PS5 controller to PS4 console

Force the DualSense PS5 controller to play nice with an older PS4 console with these two working methods.
This video shows a PS5 DualSense controller working wirelessly on the PS4 with no lag. This is not using remote play so there is no noticeable lag. As you can see in the video it works beautifully on PS4 games, the haptic feedback feels particularly smooth.
Force the DualSense to play nice with an older console.

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How to connect a PS5 controller to the console: Pair your DualSense controller to the PlayStation 5