I just bought a PC for (almost) the same money.
This is what I got:
Intel Core i7-6900K
EVGA Nvidia GTX 1080
MSI X99A GODLIKE Gaming, Intel X99
64GB Corsair Vengeance LPX DDR4-2400
1TB Samsung 850 EVO
Blu-Ray Burner LG BH16NS55
1000W - BeQuiet! Dark Power Pro P11
ASUS ROG Xonar Phoebus Solo
Prolimatech Megahalems BeQuiet! PWM
Windows 10 Pro, 64 Bit, DE
I had another 512GB SSD at home and a 2TB Normal Sata drive, so I also plugged those in.
I also bought a pretty good PC case, lots of small fans and quite silent.
The system runs well and generally I get a much better frame rate in 4k than with my SLI 980TI setup. (Cause SLI support sucks for most games...)
I should have gotten the Intel Core i7-6950X and overclocked it, but meh, I went with the slightly cheaper option.
I suggest that you get a newer CPU than the one you chose.