Jdcrank07,
Op already has a full working pc, that includes an i5-6500. He's thinking of upgrading the cpu to an i7-7700k. My point was/is that his system is unknown, he hasn't listed anything else. You can buy quite a few different models from several different pre-built vendors, and they'll come stock with an i5-6500. What they won't include is a Z mobo. You'll generally be looking at the low-grade mobo's, probably an H110. Because it's a pre-built, it'll also have a castrated bios, the only cpus that'll be supported are the ones inherent to that particular model. If the 7700k wasn't an option, it's unlikely it'll be supported, but a 7700 might.
So, barring any other considerations of scrapping everything and buying a new cpu, mobo to get better streaming results, Op just asked if he upgraded would it be better.
Op. If it's possible to upgrade, then yes, the 7700k will give much better streaming/gaming performance than your current i5, but you will need to buy a cpu cooler, the 7700k does not come with one and the stock i5 cooler is severely inadequate for the torture that streaming/gaming will be under with that cpu.