Looking to upgrade gaming PC

[Waterloo]

Originally, i was thinking of getting the i7-5820k, Asus x99-a, 16GB of ram, and a GTX 970. But, really how much better is that going to be then if i was to go with a i5 quad core? I already have a Corsair Carbide 300R, Corsair CX750M so i should be fine with those. I play all different games League of Legends, Rust, CSGO, Diablo 3, Civ5, Call of Duty, H1Z1 Dayz, everything. I am just wondering though will going for the 6 core processor make that much of a difference? I have looked around at some benchmarks but those are hard to tell most of the time because everyone uses different setups for the benchmarks. I just want to be able to play most games on high to max settings at least 60fps, would like 144 for something like CSGO. My other thought was streaming, i wondered how much of a difference it would make for that? I see a lot of streamers only have quad cores and they don't seem to have issues but i was just wondering. Also, i would like to get a CPU cooler and i don't know what i should get liquid or air cooling? My room gets hot in the summer, i don't have AC.

Edit: Also, I have 2 monitors only 1 is used for gaming, and i might be getting another. If this matters, i'm not sure.