Do these PC specs make sense for a gaming rig?

I do not like your build. Kinda sucks.

First - why and i5? i3 is about to go obsolete any day now and i5 is not far behind - keep in mind that i7 is now on Generation 7........ if Intel had been keeping its number straight that would make it an i14 today. Worse, you cannot upgrade an i5 to a current i7 later on - different case package. So, pick out a low end CURRENT i7 chip and upgrade it later on when the price of a better chip is lower.

850watt PS is NOT going to allow you to expand. Any home build, your min is 1,000 watts with 1200watts better. Keep in mind the computer is only going to use as much electricity as it needs - just because the PS is capable of 1200 watts does not mean it is going to draw that. Other thing you missed - you always want to run your PS at 70% or less, this is the most efficient and heat reducing area. 850watt is gonna be allot more than 70 percent.

For gaming - you want at least 2 video cards. 3 is best. This mother board and PS wont handle it - no room. Although the first video card removes allot of graphics math off the CPU - it is still rushed for time. Two graphics cards in sli/crossfire take turns making the graphics and doubles the resolution instantly. Add a third graphics card and #3 takes over all the PhysX and lets the other two put the cherry on top of your graphics. Instead of seeing a horse with texture - you see individual hairs when zooming in. Instead of seeing a shinny sword, you see the small nics and dents.

You don't have a fan controller with temperature monitors - these are $26 and money well spent. One temp sensor goes on the cpu, one on each video card, one on the PS.

You will need two 120mm fans pushing air in from the front. 3 pulling air out from the top. And probably one pushing air in on the bottom with a filter. Fans are cheap. You want to put them in now while the chassis is empty.

I am an IT guy. My wife is doing ESO on a ROG Rampage V MB/64gb/3 video cards/ and using a damn 65" curved Samson LED tv as her game monitor. Liquid cooled everything. Redundant powersupply. Raid 10. My rig is like hers but with less memory and a 28" monitor.

Let me share something I learned recently. I loved ESO with just 2 video cards. World of Tanks was awesome too. A few weeks I bought a 3rd video card off ebay for cheap just to test - wow - my jaw dropped at the huge difference, even on my tiny 28" screen. If you are serious about gaming - you really want to have room on the motherboard for 3 video cards. If I had a choice between buying a new video card for $600, or, three used SLI/Crossfire cards for $180-$200 each I would go with the three slightly older cards.

Good luck.

The PSU is a little high for what you need, but not by too much. A 650w PSU would be enough. Other than that, it looks perfectly fine. I'll be building something similar in a small form factor (mini-ITX) in the next month or so, once the power draw issues with the RX480 are fixed. 390 performance at the 380's price point... yes please.