Even as a girl, I think it's time you end your efforts to win her back.
You found out that she cheated on you 5 months back then and you did nothing until she came to you for breaking up 2 months ago?
I thought guys have their pride and ego but I can't see any of these left on you. You should leave some pride for yourself and move on.
What future do you honestly think you will have by being with her again? Do you think it will last? Ask yourself these. I'm quite sure you know the answer yourself.
Anyhow, good luck and all the best.