Well an i5 system would be a really fast overall PC, but an i5 is overkill for budget gaming.
I recommend getting a really good case, psu, and motherboard to build on, then grab an i3 and some cheap ram. A HD 650, 650ti, 7750, or 7770 would be plenty, but it's hard not to recommend a 7850 right now because of price/performance ratio.
A good case, psu, and mobo would provide a solid foundation to upgrade on over the next few years when you will inevitably want better performance(and have more $$$)
An i3 will provide a strong upgrade path to get an i5 or i7 later.
or....
You could get an A10-5800K/6800K now with a fm2+ motherboard. You could handle 720 gaming now without a video card, and you could upgrade to Kaveri next year or so.