The majority of gaming laptops use a i7 quad core. These typically are rated for 37 or 47 Watts (vs 15 Watts for the standard U dual cores) and cause a major reduction in battery life. The two laptops with discrete GPUs which have the longest battery life get around this problem with a humongous battery (93 Wh for the Dell XPS 15, 95 Wh for the Macbook Pro 15). Unfortunately both use badly outdated mid-tier GPUs (nvidia 750m).
Most other laptops with a discrete GPU and i7 quad "only" have a 40-50 Wh battery. That will typically last about 4 hours with light use. The Razer Blade has a 71 Wh battery, but only manages about 3.75 hours. The Gigabyte P35W has a 76 Wh battery, and supposedly can last 5-6 hours of light use.
If you're willing to lose the quad core, you shoudl be able to get substantially better battery life. Several gaming laptop models have options for a i5 (the mobile versions are all dual core) or dual core i7 (model number ends in a U instead of a QM). If you can find a laptop which meets your specs with one of these processors, it may hit your 5-6 hour target. Otherwise you'll have to learn to live with just 4-4.5 hours of light use (obviously you can extend that a lot if there is lots of idle time - the aforementioned Razer Blade will go 6.3 hours idle).
Also, try to stick with a 970m or 965m. Those use the second gen GM204 Maxwell core. The 960m uses the first gen GM107 Maxwell core. The differences aren't major, but I assume nvidia optimized Maxwell after seeing real-life data from the first gen.