OP [BlackAzrael]
I have used a PC since I believed one could do something, and that was around 1984 and began working in the computer industry in 1986, over 30 years ago. Also, I worked in the PC industry for a very long time. I designed and built computers, repaired corporate computers and PCs and advised companies regarding computer problems or upgrades, among other things.
As a hobby I began overclocking at least 25 years ago, both for myself and others.
Now that some of my background is out of the way I will say that some of the comments here are instructive some are not.
I had an Intel i5 3570K that overclocked stable at 4.7 GHz and found that there was no reason to go beyond 4.6 for Microsoft Flight Simulator X, a very CPU intensive program [I used to be a commercial rated pilot and used FSX to help keep my skills honed at no cost except the program itself]. For the rest of gaming 4.4GHz was fine and 4.0GHz and my MSI GTX 980 Ti Lightning was good enough for my 40 inch 1080p monitor two feet from my face. I will admit that a 4K monitor looks very good, however, I am now disabled and do not have the income I used to for computer and monitor upgrades.
Now to your situation. You did not mention what CPU cooler or computer case [important for airflow for cooling] you own. A good air cooler will perform as good as most of the best water coolers. After a period of time the liquid in a water cooler slowly heats up, once hot it stays at that temperature for a relatively long period of time, even after a long benchmark run or heavy CPU load gaming. It warms slowly and cools slowly. On the other hand a good air cooler with good TIM heats very quickly and cools very quickly after heavy CPU usage. The biggest downside to a large air cooler or internal water cooler is enough room for either cooler.
There are three things that are important to overclocking that you did not mention, two of which is in my previous paragraph, the other is system memory or RAM. Lower voltage RAM is much more important to CPU overclocking than higher speed or overclocked RAM. Higher speed RAM and overclocked RAM require more volts, which reduces your CPU overclocking ability, as does a good air cooler and proper computer case to dissipate heat.
Because my Gigabyte motherboard was failing after 5 years of CPU overclocking I was forced to upgrade on February 10, 2017. I purchased a Gigabyte Z270X-UD5 because it is a solid motherboard for overclocking and uses dual Intel GbE LAN among other things, an i7 7700K that I delidded and used Thermal Grizzly Conductonaut between the CPU die and inside the "lid" to lower temperatures with the CPU running at 5.2GHz, Noctua NH-U14S air cooler, 32GB of Corsair Vengeance LPX 2666 1.2 volt system memory, and Windows 10 Pro [that I had to "fix" many things to make it less of a resource hog and much more secure]. The price for all of this was just over $1,000 U.S.
My 5 year old Cooler Master HAF 922 computer case was retained because of it's great air movement to keep everything inside cool, including three 200mm case fans.
There is a problem with the i7 7700K [and AMD's higher end CPUs] and that is heat - they get very hot when overclocking, even with a good cooler. With this CPU at 5.0GHz Microsoft Flight Simulator X, with the add-ons I have running, is probably the most demanding program [game] on the CPU and does great over large airports and cities at low level, such as KLAX [Los Angeles] or EGLL [Heathrow {London area}].
What is dismaying is that at stock speed the I7 7700K does not perform much, if any, better than my i5 3570K with all 4 cores overclocked to 4.5GHz running FSX with add-ons.
And, remember, most i7 7700Ks begins getting very hot beyond 4.6GHz. If you find yourself winning the "Silicon Lottery" and are able to get the CPU to 5.0GHz temperatures will not get as high, however, almost no i7 7700K CPU will get to 5.0 GHz at 1.200 volts, so, good luck with that.
I mention all of the above not to confuse you, rather to let you know at least some of which you will need in hardware if you move to the i7 7700K or higher end AMD CPU and overclock for CPU intensive gaming. Also, the i7 7700K does not come with a cooler, you need to purchase one separately, and even at stock speeds that CPU gets toasty requiring a good cooler.
Currently at 5.0 GHz the i7 7700K is the gaming king, with only a couple of exceptions that yield a few more FPS with a CPU with more cores [and those being overclocked].
I suggest that you keep the i5 3570K, put a good cooler on it, such as a Noctua with a large fan. Mine does fine, the largest will drop max temps another 2 degrees or so off of maximum temperatures. You can purchase a newer Noctua for your current CPU and it will fit the i7 7700K, and Noctua is the easiest cooler to install, even though some companies have copied their mounting device - just enough to keep from getting sued for copyright infringement. [Note: I used the Noctua NH-U14S because it is good and is the largest that will fit in my case with a 200mm fan in the side of the case.]
To summarize, keep what you have with the possible exception of purchasing a larger case and a Noctua cooler for your CPU, in preparation for a future CPU upgrade.
EDIT: Using an i7 will improve game FPS with the CPU running at least 4.2GHz on non-CPU intensive games, that is, more demanding of the video card [Heaven benchmark is a good example], with your motherboard look for an inexpensive i7 3770K, around $50 U.S. that will easily overclock to 4.2 to 4.4GHz [with a good air cooler] - ask the seller if the CPU will overclock. An i7 3770K that will overclock to 4.6GHz full time and stay below 70 degrees C using a good cooler is a good investment.
I'd be happy with 4k play, over 8k is an overkill for space and money for me but happy that there are people that demanding 
