Should I upgrade my CPU and GPU?

If you put a i7 7700K in your motherboard make sure you go to Gigabyte's web site and download the latest BIOS, and make sure it will support the i7 7700K.

Board revision 1.1 http://www.gigabyte.us/products/product-page.aspx?pid=5833#bios
Board revision 1.0 http://www.gigabyte.us/products/product-page.aspx?pid=5497#bios

The revision number should be in one of the corners of the motherboard, probably near the last PCIe slot, and should be labeled Rev. 1.0 or Rev 1.1

Note that some people have not been able to overclock the i7 7700K as high as an i7 6700K in Z170 motherboards, and the i7 6700K is less expensive.

An outstanding cooler: Noctua NH-U14S http://techbuyersguru.com/noctuas-nh-u14s-and-nh-d15s-cpu-coolers-take-best?page=2

I disagree with Adrian Ocampo. Thermal compound does make a difference in lowering CPU temps. I started working in the PC business in 1986 and have worked on just about everything PC related, including overclocking. There are some good thermal compounds. For the past several years I have used GEID GC-EXTREME, it is a very good thermal compound and easy to apply. It comes with an small aplication tool, however, do not use it. Properly spreading most compounds with a tool like that is difficult. The best method is NOT to make a grain of rice or pea size amount. The best method is to use THIN lines in the form of an X over the CPU lid; that provides the best coverage and does not apply too much paste, which actually increases temperatures.

Note: When finished using the thermal compound stand it on end, with the tip down, as you would find it hanging on a store shelf. Thermal compounds, such as this one, uses an oily type substance and it migrates to the tip if the tube is laid on it's side. You do not want something that looks like oil coming out of the tube, you want thermal compound. I use scissors to cut along the package side and that allows me to place the TIM back in the package when finished, it is easier to stand on end while in the package. I will not go deeper than that in explaining.

If you want to keep your motherboard and overclock I suggest getting an i7 6700K. You should not have to overclock it to get great GPU performance from the fastest video cards however. Most games do not get much of a boost from 4.0GHz to 4.6GHz. You can have a non-overclock set up in the motherboard BIOS and an overclock setting for CPU intensive games, that way you will not be running your CPU at 4.5 GHz or whatever all of the time. When you turn on your computer simply hit the Delete key, enter BIOS and select what you have saved and then hit the F10 key to save and reboot your computer. Your motherboard will live longer this way.

Keeping the CPU cool is still important. It takes more electricity to make electrical devices function efficiently and properly at higher temperatures. I was going to provide an example, however, it was taking too many words and I do not want to write a book. And, I believe your motherboard only has 4 CPU phases [mosfets], so, keeping electrical supply to a minimum over a long period of time is even more important. Electrical power is split between phases, so, make sure all of them are in use for motherboard longevity and to keep the CPU cooler. Many motherboards have 8 CPU phases and some have 12.

As to your question, should you purchase a faster CPU; your CPU is boarder line for the most CPU demanding games when using a very fast GPU. If you want to play those games, then a faster CPU is a good investment. If your games are not very CPU intensive then upgrading will not do much for your fps.

Regarding game FPS, often the MINIMUM frames per second are more important than average. Some games do fine with a min frame rate of 25, other games need 60 fps [if your eyes are good enough].

I will provide a link comparing an i5 6500 to an i7 6700K. Look at the i5 side of the screen and look for chop, color distortion or any distortion in the game. If there is none for the game types you play, then do not upgrade your CPU, purchase a GTX 1080, or wait for the fast ATI cards coming out in the next month or so. [NOTE: I do not like the fact that the game is played on a 1440p screen. The benchmarks should have been run on a 1080p as well because that resolution is by far the most used, and it would have made the video card work less hard.]

Unfortunately, BF 1 is not in the benchmarks, none the less, your current CPU should do fine with that game.

https://www.youtube.com/watch?v=x02w_3GeuKY&t=0s

Battlefield 1, @ 1080p:

Note: Watch for CPU % usage, lower is better

https://www.youtube.com/watch?v=gDnPDjIt18s [GTX 1070]

https://www.youtube.com/watch?v=YtxuKEbNRrw [ATI RX 480]

https://www.youtube.com/watch?v=mfADEPQloDw [GTX 970]

https://www.youtube.com/watch?v=BQUSq2N6218 [i7 4790K, GTX 970 vs 1070 - 1080p / 1440p / 4K]

https://www.youtube.com/watch?v=2J_BxV5CPfY [GTX 1080 OC/I7 6700k 4.6Ghz]

That is a lot of information and I hope it helps you make your decisions.