No way, that i5 could handle a dual 7970 setup without bottlenecking at all. Of course you'd need a new PSU but that's another story
My suggestion would be to either get :
- The 7750 for 110$ on the current 300W PSU.
- 6870 http://www.newegg.ca/Product/Product.aspx?Item=N82E16814131378
for 170$ and CX500 for 60$ http://www.newegg.ca/Product/Product.aspx?Item=N82E16817139027
Total : 230$
It's your call
The 7750 will give decent gaming performance but will have trouble with games like BF3 with cranked textures on resolutions of 1080p and higher.
EDIT : those are the .ca prices, they'll be even lower in the USA.