The PlayStation VR will run on PS5, but you need an extra accessory first.
You Shouldn't Worry About The PSVR 2 Headset Having A Wire
Contains: PlayStation VR headset, Processor unit, PlayStation VR headset connection cable, HDMI cable, USB cable, Stereo headphones, AC power cord, AC
Sony PlayStation VR
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PlayStation VR 2 headset for PS5 has JUST been announced! Check specifications, game and more
Controller Charging Dock for PS5 VR2, PSVR 2 Charging Station with VR Headset Holder Display Stand, PS VR2 Controller Charger for PSVR2 Accessories with Led Indicator, 2 Magnetic Clasp & Type-C
PSVR 2 Review: The Best VR Gaming Experience With Strings Attached - CNET