Well the 5820K is clocked @ 3,3GHz stock. That means - lower performance in CPU-limited games but better performance with x264 (what is used in OBS) and generally more power for multiple tasks while gaming. If you overclock it, the performance will rise, but also the power consumption and heat output.
You will need an aftermarket cooler that can handle 140W+ output (generally start with twin tower 120mm, better twin tower with dual 140mm fans or 240/280mm AIO watercooling unit). That will hit you for like 50-100$. Right now i`m cooling it with the NZXT Kraken X61, one of the most expensive AIO units out there, way over 100$.
I also got a top tier CPU, that is capable of reaching 4,5GHz with decent voltage (its in the top10% range) and i could sell it for way more than i paid for it because its a great overclocker.
Then you will need DDR4, a quad channel kit (since the 2011-3 socket actually can use quadchannel memory).
That will set you back another 200$ for the cheapest (dont know the prices, specially in UK).
And a X-99 board will set you another 200$ for the cheapest. But they are high end boards, even the cheapest - this is the Intel Enthusiast socket, so even the cheapest boards offer SLI/Crossfire, M.2 slots and other nice things.
I use the ASUS X-99 A (cheapest ASUS board with this socket), 16GB of Crucial Ballistix Sport DDR4 RAM (mostly because it works and is low profile, allowing me to install tower coolers, most of "popular" RAM brands offer huge heatsinks on the sticks). You also want a good PSU and a nice case to allow enough airflow to cool the board and provide cool air for the CPU cooler.
Like i said, 1000$ is a good starting point for i7 5820k + everything needed.
This means you will have to replace (maybe sell) your RAM, CPU, Board and maybe other things like PSU, case, cooling and more, increasing the cost.
The problem is not the i7 5820K (its the best bang for the buck CPU from Intel right now when looking at the i7), the problem is anything else needed to drive it and maybe overclock it :P