Yes! You should be able to download and play Rec Room on PlayStation 5.
Furthermore, you are able to play Rec Room using a PlayStation VR headset that is connected to a PlayStation 5, provided that you have the camera adapter. See more information about this here.
At the moment, there are no specific enhancements present on the PlayStation 5 version of Rec Room. However, you will benefit from faster loading times and more stable performance by default due to the PlayStation 5's better hardware.