Random process taking a lot of resources

I'd leave it. It indexes packages so you can search them quicker. It shouldn't take very long, possibly the first time it runs it could take a bit longer, wait until the box has been running a few days and see if it still chews up cpu/ram. (IMHO I wouldn't say 5 minutes is a problem)

I don't really search packages, I know exactly what I am going to install when I go to do it. It may be fine for now but definitely not once I have a site and several real time game servers running on the box. From what I read about it, they said this issue was patched in 2009 but clearly it isn't so it doesn't seem like something that will show up in the next release of it, so if I can remove it without breaking anything I will probably end up doing that.

You can remove it with aptitude remove apt-xapian-index nothing in the core system depends on it so you should be fine (I just tested removing it and it didn't break anything)