Can a relationship truly survive being cheated on?

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Sorry if the thread subject doesn't make total sense, I couldn't really find a good way to word it. :/ Anyways, five weeks into my current girlfriend and I dating (It's online, make fun of me, trust me I can guarantee I've heard worse and I couldn't care less), I found out she had been cheating on me, I'm not sure for how long, and I want to say it wasn't for the whole relationship, but I honestly can't say. Both her and the guy she was screwing around with said it only recently started happening. After I caught her, we had a huge fight, then we 'made up.' I took her back, I forgave her, and I know she hasn't been cheating on me since. (I don't really care to share the details on how I know, just isn't importantppo.) Anyways.. that was, well, about 5 weeks ago.. I know I shouldn't have forgiven her nor taken her back so easily, let alone at all, but the thing is, she is literally the only person that makes me smile like she does.. It's been such a short amount of time, but I love her..

Anyways, my question is from experience can a relationship survive and succeed after an incident like this occurs? I'm really only looking for peoples opinions that have been in relationships where they got cheated on, or where you cheated. Keep in mind, I'm not looking just for people still in relationships, not all relationships that have something like this happen end because of this..

I'm really torn because of this, and so far no one has supported me in having taken her back, I don't care for other peoples approval.. I just want to know if there is even a chance...