People tend to use lengths of time to justify misdeeds in a relationship. 5 years is a long time to be with someone, but it's also a drop in the bucket in the long run of your life span.
Trust can be rebuilt in a relationship if it's lost, but it takes both partners to work on it and truly forgive. It sounds like now you're on the fence as far as forgiveness. Maybe it's due to the fact that the pain is still fresh. But look at it this way. You said she was mad because you were too hungover to hang out with her. Okay. We've all been there. It's not a prerequisite to hang out with a significant other all day every day. You were sick. Shit happens.
Now look at what you're mad at her about. Stepping out of the relationship. It's not like you missed hanging out with her because there was another girl in your bed.
People cheat because there's essentially something missing in the relationship. As far as I'm concerned, alcohol is no excuse. However, her telling you right away could mean it was a mistake. Mistakes happen. At this point, don't worry about how she is going to react when you talk things over. It's time to take care of yourself and see how you really feel about your relationship. If you don't think you can rebuild trust, then it may not be worth it to push along in a doomed relationship. If you think you can leave this incident in the past, then it's going to take a lot of work on both your parts to leave it there.
But if making out with someone else is a dealbreaker to you, I think you know what to do. Let us know how the talk went if you feel like it.