I think if one person continues to consider breaking up then something is very broken. The cheating might be creating a guilt complex that’s hard for her to overcome. If you guys manage to patch things up I’d seriously suggest couples therapy to work through the base anxieties that keep her thinking about calling it quits.

I think the fact that you guys are opposites in what is fun and what you value and especially at your age makes you both incompatible. It such a that you’ve been together for 5 years but if it’s not making you both happy, then you guys should find what makes you happy. I’m sorry OP but I’m sure you’ll find someone who is more in line with you and what you want (and that won’t cheat on you because no one deserves that). Good luck!