I'd agree with Skitz, the 3570k is one of the best gaming processor available right now. I'd also agree with Lostgamer_03, overclockit to squeeze every last bit of performance from the processor. If looking for a moderate overclock consider the Hyper 212 EVO.
Thanks Skitz! The i5 3570 is perfectly compatible with my new MoBo and graphic cards?
There is a difference between a 3570 and a 3570K.
Both are compatible with your motherboard.
The "K" lets you easily raise the multiplier from 34 up to about 43 for a nice increase in cpu power.
A 3570K is entirely appropriate for your 7970.
Each represents the best in category for gaming.
If you live near a microcenter, they will sell you a 3570K for $170.