Firstly, you're 15 right? And I THINK you said five years ago you loved her. Meaning you were 10? I'm not so sure but can you be in love with someone when you were 10? Someone clarify me on this.
Secondly, this is for a week or three months? I'm confused on that part.
Thirdly, since you're going to be living in the same house and you try to explain to her that yes, you have not had much contact in a few years but you want a 'fling' will most likely not go down well. You could be setting yourself up for a week/month of awkwardness and hurt. What happens if she tells her parents (I assume they live there too)? They may send you back home or kick you out completely. Two 15 year olds, assuming she's the same age, having a, as you put it, 'fling' will not go down well with parents.
Fourthly, let's say this works out. Let's say she agrees and you do whatever you want to do then you have to leave. What then? You part ways and possibly never see her again? You felt bad enough not knowing if it would work or not but now you're going to part ways while you're both happy and really having feelings for one another? How would that help, exactly? I understand the closure thing but really, won't this just cause more problems? Unless you be with her from the time you start dating to which you don't want to be with her any more, you'll still wonder what may have happened.
In conclusion, I think this is a bad idea. Yes, you may like her and she MAY like you but don't force something to happen. Don't go up to her and say something like "Hey. I know we haven't talked in a while but how about a summer fling?". It will most likely NOT go down well. And even if it does, you will probably just feel worse at the end of it. Especially since you're 15 and probably don't have a way of seeing her regularly. Plus you'll probably still want to have a shot at a long distance relationship and she may, or may not, find someone else in the mean time. Who knows.
Of course, you don't have to and probably won't follow my advice but that's what I think. Good luck either way and I hope you inform us what happened.
