A lot depends on just exactly what games. At 4k resolution playing WoW, the lowly r9 270x gets better frames than a gtx 970. Take that with a grain of salt if you wish.
There are always exceptions to every rule. Ya'll say the i7 is useless for gaming, only 1-2 frames more? In what games? In BF4 multi-player the i7 beats the hell out of an i5, as does the fx 8350. This is true for any mmo or similar multi-player game. It's only on the single player that there's only a 1-2 frame difference.
Pound for pound, the i7 is equal to or beats an i5 at anything. Is the i5 enough? Yep, and deservedly so. A strong i5 will handle any game pretty damned well, single gpu or sli/CF. The i7 will handle it better.
As for the 5820k, Op is gaming on a 4k monitor. That's not exactly a budget oriented decision, so tight budget isn't too much of a concern. The only reason it doesn't game as well as the 4790k is its relatively slow clock speeds. OC it to 4.5(1x core) to 4.1(6x cores) and then tell me it sucks compared to a 4790k. Yeah right.
Gta - V reps state a 4core cpu minimum. However, the game plays just fine on a Pentium g3258 if you get the clocks up. Many games play just fine on an i3 with HT enabled, almost as well as an i5,better than some i5s actually considering the i3's faster clock speeds.
Ya'll are missing the point somewhat. It's not a topic of how little can op spend to just settle for 2nd best because it's 'good enuff'. OP is looking for best performance. Question is, does op have the wallet for that, and the knowhow to get it, because the 2011-3 will be stronger for longer with a good OC, the i7 is good now, and will have benefits if Op branches out of 'just gaming' vrs i5.
I bought an i5 for me and my games. My wife now works online from home using Citrix (sheesh) and is currently Photoshop crazy. Wish I'd spent the extra for the i7, but I was repeatedly told, 'an i5 is all you need for gaming'. Yeah. Just goes to show what happens when you settle for good enuff.