Go to the link in my sig it is also the sticky at the top of this forum.
But to answer your question it might but its cutting it real close recommended is 650 watts. And for the 5970 I wouldn't mess with your spending $700 on that card so dont skimp on the power get atleast a 650 watt.
Most likely it would. Corsairs are about as stout as PSU's come. They are one of the few to actually underrate their power supplies output. But it wouldn't hurt to throw another $25 at it and give yourself some breathing room.