I really need google out of my life but I can't see that anything other than pixel phones are supported according to the web...
What would happen if I installed graphene onto a fairphone 5?
well first, you can't. You would need to build an image that is able to run on a Fairphone. Second, Fairphone uses outdated, insecure hardware. They also don't follow best practices. Like shipping avb test keys in production builds. I would stay away from these phones personally. There is nothing good about them.
Would it work? Definitely not. Would it brick your phone? Maybe, if you try hard enough.
If you want GrapheneOS, you're going to need a supported Pixel. You could get a used one, or from a reseller, if you just want to avoid transacting with Google.
If you're unwilling to use any device made by Google, then you'll need to find a different OS.