When processing video data, there are two ways:
- software using an encoder (x264)
- hardware assisted using an encoder built in on a GPU card (NVENC Nvidia, for example)
Your Nvidia card doesn't have an onboard NVENC chip to help you. You can either go out and buy a higher end GPU card (like the Nvidia GTX 1060 or better) or use x264 which is a software driven approach to encoding. That requires, however, for you to have a strong CPU with multicores/multithreads. Your i7 5500 is behind the times as it only has 2 cores and 4 logical processors on it. Today's CPU has way more than that, typically 4 cores and 8. And the newer CPUs like ThreadRipper and i9 have even more yet.
Value wise, the AMD Ryzen 1600 CPUs offer the best price to performance so I'd suggest going that way if you choose to move forward. Given the specs I've seen and the benchmark results on your CPU, you are going to end up with low looking quality output, especially if you push it playing highly animated games. If you are playing say, a crossword puzzle, chess, checkers, or any application where there is not much animation, you may be able to get by. But sooner or later, you are going to see that you will need a new computer.
Also, before you consider spending a lot of money on a new one, make sure that you have sufficient Internet UPLOAD speed. Everything being streamed from your computer goes upstream to servers. That connection must be at least 5Mbps upload to get an ok looking 720p stream. If you have 7Mbps, that's even better and the quality will show. If you don't have a good upload speed, its really not worth getting involved with streaming and throwing money at it. Just want to put that out there just in case.