For gaming, the i7-6700K is about the best you can buy today.
Few games can use more than 2-3 cores, hence the I5(with an overclock) recommendation from others.
The extra 4 hyperthreads of the i7 will no be used for gaming.
However, with your budget, I recommend the I7-6700K. At stock, it has a higher clock rate so no overclocking is required.
The clocks on the 5820K 6 core are at 3.3; the i7-6700k are at 4.0(stock) and the performance per clock of the i7-6700K is marginally better.
Most games are heavily dependent on a few fast cores.
And... for editing, the i7 hyperthreads will be useful for most apps.
Buy a Z170 motherboard to permit overclocking.