Firstly, five months is long enough to establish a relationship that'll survive a mere summer break. I say that as someone who's spent four out of six years in a long-distance relationship, not counting the summer breaks when we went to the same college. By our first summer break, we'd decided that we wanted to see if we could move our relationship towards engagement (nothing official at the time, but we liked the idea and kept it as a mutual aspiration). Long distance relationships are only quick to break up by default when it comes to high school graduates.
Secondly, even if they do break up, there's an unwritten rule among most people that you can't date someone if they went out with a friend of yours, especially a best friend. Granted, some people don't follow it, and I think it's bullshit to not do it simply because "You just don't," but my point is that she may not think it's right to date you, no matter how long of a cool-off period you give her. She'd have to REALLY be interested in you to overcome it in that case.
And, of course, if she's completely willing to go out with you, then you have to be careful. Either that means you're a rebound or she's not very committal.
In short: Hope all you want, but don't expect anything.
