Sony has released a driver for the DualSense controller that allows the PlayStation 5 controller to be used on Linux.
Earlier this month, Sony released the driver. However, the driver has not yet been officially accepted and so has yet to be rolled out worldwide, but this should be done in the near future.
Thanks to the driver, all the basic features of the PS5 controller will work properly on a Linux operating system, including the regular action buttons, the touchpad, the default rumble and motion sensors. The haptic feedback and adaptive triggers are not yet working.
No official drivers for the DualSense are available for Windows. However, the controller is supported via Steam.