True, and it crosses over quite naturally with the other pair of characters.
OP, I assume you'll be playing locally with your girlfriend? RE6 co-op works a bit differently locally (i.e. better, since you can trade ammo and stuff) so bear that in mind. Not sure how/if RE5 differs locally.
I'd recommend both. You can get RE6 for £8 off Amazon UK, and RE5 Gold for about £10. In terms of story, 6 isn't really a continuation although it does use some of the same characters or refer to some of the same organisations and so on. If any RE game is recommended before playing these in order to understand the story, it's gotta be RE1 and RE2, but they're VERY different types of games and aren't co-op.
I'd suggest 5 Gold if you want a more challenging and fun experience with a touch of survival horror (nowhere near the previous games though) and 6 if you want a more shooter-like experience. I've been enjoying 5 Gold more myself, but I AM a strange person (and playing single player), so I don't know if that matters at all.
My post gets modded a year later (metaphorically posting) in an essentially dead board? Haha. I know who is responsible for this so I am content. It's not Lefties that reported it because he took it like a champ.
Human beings want to be controlled. They forsake those who offer no benefit. They laud those with power! They can do nothing for themselves!- Dauragon C.Mikado