So let me get this right:
1) a massively overclocked, newer i7, with 6 cores, 12 threads, 15 MB cache, and possibly much faster DDR4 2133 memory
slightly but noticeably beat
2) an older i5 with 4 cores, 4 threads, 6 MB cache, and at best DDR3 1600 memory.
And you automatically assume the difference was because of the core count? Too many variables. Unless you are multi-tasking (gaming + streaming for example), I still haven't seen anything that shows more than 4 cores helps gaming. They are almost always an apples-to-oranges comparisons where the chip with more cores also has many other advantages, so we can't really see the exact difference that the cores have on gaming.
I'm with the others. Keep your 6700k until it is too slow for gaming. Then determine if it is a core count problem or not when you get a new chip.