On the Pixel 5 the rear case is actually the complete housing that holds all of the internal components of the phone. So if something is coming apart it's the screen rather than the rear case that is separating. As @bp159 mentioned, the most common cause for this is the battery swelling and pushing the screen away from the frame, assuming the phone hasn't experienced damage and the frame is actually bent.
You'll need to open the phone up and check the battery. If it appears pillowy and there's any softness to it, then the battery has reached the end of its life and must be replaced. Batteries that are swelling can be a fire hazard, meaning your phone can literally catch on fire - ask anyone who owned a Galaxy Note 7. A normal battery will be square and solid; you won't have any trouble telling the difference once you have the phone open.
Really, all you need to fix this is a sheet of display adhesive, assuming the battery is okay. This is the part being sold here on iFixit; it's a genuine Google part so it's as good a quality as you can possibly get.
Google Pixel 5 Display Adhesive - Genuine
If you end up needing a battery, then iFixit has you covered there too.
Pixel 5 Battery: Genuine Part / Replacement Kit - iFixit
I'd recommend getting the Fix Kit version; for an extra $7 USD you get all the adhesives you need plus every tool required to do the job right. And of course instructions on how to replace the battery would be handy too, right? Welp, here you go.
Google Pixel 5 Battery Replacement - iFixit Repair Guide
Take a look at the guide then let us know what you find, and if you have any questions feel free to ask!
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