PlayStation 5 does support PlayStation VR, but there is a catch. While there's no new headset built specifically for the next-generation system yet, and the brand new PS5 camera doesn't even work with the PlayStation VR.
If you want to use VR on your next-gen console and play every PSVR game but Robinson: The Journey and DWVR on PS5, you'll also need a special adaptor to use with your PS4 PlayStation Camera. You can't buy this PlayStation 4 Camera adaptor for PS5 in stores though, you'll have to get it straight from Sony.
If you want to use PSVR on your next-generation console, this is what you'll have to do:
The official description for this adaptor explains that "this allows the use of PlayStation VR when playing supported PS4 games on a PS5 console, including games that require PlayStation Move or PlayStation VR aim controllers." If you want to experience great PSVR games like Iron Man VR on PS5 or use VR in games like No Man's Sky after the substantial next-gen update, you'll need an adaptor for your camera.
A new camera will be available on November 12, but it is not compatible with PlayStation VR.
Step 1: Find your PlayStation VR's serial number
While this seems obvious, it's still worth noting that you need to have a PlayStation VR and PS4 Camera and know the VR headset's serial number before you can request an adaptor from Sony.
You'll need to submit your headset's serial number as you're requesting an adaptor. This is found on the back of the headset's processing unit at the bottom-center. Once you know what this is, you're good to go.
Step 2: Fill out an online form to get the adaptor
In order to actually get a PSVR camera adaptor for your PS4, you'll have to fill out an online form for Sony. As we mentioned, the form will have you input the serial number of the headset, though you don't need to include any spaces or dashes. After that, you'll be prompted to give Sony your shipping address, name, and phone number and can submit the form.
After that, North American users will be on a list to get a headset in "mid-November" according to a support page. It's free, so all you have to do is fill out the form to get one. While there isn't a guarantee that you'll get it by launch day, by the end of the year you should have the ability to play your favorite PSVR games on PS5.
Now, Sony just needs to release a new headset that's compatible with the PS5 Camera and doesn't require players to ask for an adaptor in this roundabout way.
PS5 will be released on November 12, 2020.