Using a 5970 on the rig you have now, and a top of the line i7 overclocked to 21jiggawatts, you wouldn't notice the blindest bit of difference, I mean, at all, not an iota, no one on earth could tell the difference between the "fastest" computer in the world with a 5970, and your rig with a 5970.
Ok, I'm assuming your cpu can do, a good 3.5GHz, so the few very single thread limited games have a little headroom as at stock it could be a little slow in those games.
In the vast majority of newer games you'd have no issues.
This is by no means, every game in the world, or even close, but its a general trend the majority of games follow, that is, being severely GPU limited.
http://www.legionhardware.com/articles_pages/metro_2033_performance_guide,9.html
965 at 2Ghz, same FPS(ever so slightly higher, you'd NEVER see it but its funny anyway

) beating a 4Ghz i7, and a 2Ghz i7 matching in every way that matters, a 4Ghz 965.
Its all about the gpu, its always been all about the gpu, the few situations people don't run the resolution settings high enough you'll start to see a difference, but thats when you run say Metro 2033 at medium settings, at 1280x1024, show me a person who has a 5970 who runs those settings, and I'll laugh at them, as we all should, as he complains he's cpu limited.
The fact is NO MATTER the gpu you have, you adjust the settings and resolution till you're gpu limited, otherwise you're wasting the GPU.
THe very few CPU limited games, the first Sup commander, a couple other RTS's and FS maybe, your quad will still only be marginally behind a i7.
If you essentially have the cash to get a i7 setup and a 5970 ontop, you basically have the cash for 2x5970, and that will give you double the performance of the i7 + single 5970 setup.
I would recommend though, 2x 5850's, overclock further(probably) save a bundle, see probably higher performance with the better overclock, quite a bit cheaper at the moment. Thats assuming you have the slots for xfire and mobo supports it.. on that subject does a mobo need to support xfire, or do all dual pci-e slot boards do xfire and only SLI is not allowed on certain mobo's?