I have a 4790K that I use for gaming as well as other multi-tasking, and it does it's job perfectly. If you're mainly going to be using it for gaming, I would recommend going with the 4790K. The higher clock speeds will likely be more of an advantage than the extra cores in a typical gaming scenario. The 4790K is also a few hundred dollars cheaper as well.
The other components will also be cheaper. If you go for the 5930K you will be needing DDR4 RAM, and the a supporting motherboard as well.