With all due respect to @uchetil, I think Juan Garcia has it wrong. Many Android phones like Samsung have two different ways to replace the screen; one, you can buy just the screen by itself, detach it from the phone's frame, then reglue the replacement on. The other way to do it is to buy the screen already attached to the phone frame and basically gut the old phone, moving all of the interior components to the new screen+frame assembly.
So it's understandable that when you're talking about the frame, they thought it was like a Samsung. It's not; Pixel phone screens are not available already attached to the phone frame, and you can't access the interior parts without removing the screen.
Anyway, the frame you're talking about is the mounting frame for the screen that isn't supposed to come off the screen. What's happened is that instead of getting your opening pick between the frame and the phone, you ended up inserting it between the screen and its frame. If you look at the Pixel 5 Screen Replacement Guide, on Step 2 it specifically cautions about where to insert your pick, which is exactly where you went wrong. Here's the picture and text from that step.
- Screen seam (red): This seam separates the screen from the rest of the phone. Do not pry at this seam.
- Bezel seam (orange): This is where the plastic bezel designed to protect the screen meets the frame. It's held in place by plastic clips. This is where you should pry.
The fix for this is to simply repeat the opening procedure on the frame that's left on the phone. And no, you should not attempt to remove the frame from the new screen; you'll almost certainly damage the OLED display if you try. Since you can't use a suction cup, get it started by prying up from the inside until you can get an opening pick in, the proceed with the normal slicing of adhesive process. Once you have the frame off, you can then continue with the normal steps of the guide. Be sure to clean off the old adhesive from the phone and be careful installing the precut adhesive; it's not very forgiving so you'll need to get it place on there correctly the first time (I usually buy a spare just in case).
Good luck, and let us know how it all turns out!
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