thats backwards from the normal consensus. you can do AMD cards (or nvidia) together because the driver is the same... although you'd be stuck on 12.4 since the dx10 cards were just dropped. Its generally NOT recommended to do an nvidia and AMD card together because of driver issues. technically it should work but its a hell of a lot easier to just use cards from the same manufacturer.
That being said there is no reason not to run them both off the 5970, and its the better way to do it. the 2nd display sitting at the desktop is not going to affect FPS at all. And you can't webbrowse without alt tabbing out of the game anyway. all though you could leave a page up to reference etc.