Depends on the resolution and game. At 1920x1080 to i5-6500 will hinder the full potential of the GTX 1070 on CPU intensive games. At 4K your CPU won't be a problem.
Given that all the prices for GTX 1070 (in stock) are insane right now and you can find a GTX 1060 6GB at less ridiculous prices. I'd lean towards getting a GTX 1060 6GB.
Don't get stuck on a GTX 1060 a Radeon Rx 580 8GB has very similar performance averages. If you can find a better deal on one of those. Then get one. They have the advantage of Freesync monitors being much cheaper than GSync monitors.
If you have a Microcenter near by. Watch their prices. Of all the stores I'm aware of. They have the best prices on the GTX 1060/Rx 580. I just picked up an RX 580 8GB...