The quickest way to turn off the PS5 controller is via the Control Center. Press the PlayStation (PS) button at the center of your controller between the two analog sticks to bring it up.

Next, scroll to the Accessories menu and press X on your controller to select it. It’s the icon with a gamepad and a battery meter.
You will see a list of every accessory currently connected to the PS5. The DualSense will appear as Wireless Controller. Press X again to select it, then choose Turn Off to put it to sleep.