The sad part is, if the two of you hooked up to the same router, you’d not only experience lag, but lag 10 times worse since you’re sharing the same bandwidth. Not that I’d recommend you do that since you can just play 2 player mode, but it certainly helps give an understanding as to why you get lag in the first place.
You might think data is sent right down the wire spreading the distance of those five miles, but that’s not exactly how it happens. Instead, everything you do gets sent to a PS3 server for data mining or whatever else Playstation feels like doing with it (Security purposes I’d presume), processed, and sent along to whoever requested/needs it (The other player). This could mean that A) the server you’re nearest to is a kagillion bazillion miles away, B) your internet is actually quite bad like Pisko said, or C) your area is hit with huge traffic between you and the server, completely ruining whatever experience you might hope to have with one another since if it happens to one of you, it happens to the other.
Sounds like a case of bad luck to me. Sorry man.