Streaming takes a lot of CPU, so much so that most "professional" streamers end up having a second PC to take care of that load with a video acquisition card to get the image from their Gaming PC, so that it doesn't affect their in-game performance, and the usually have a beast of a PC in the first place. I don't like to repeat myself, but if you're gonna stream using your CPU you need at least a quad core i7. There is, however, an alternative, you can stream using GPU. The quality is not as great for the same bitrate, but it is, as far as I've experienced, less taxing.
Well, you can stream with a lesser CPU, but you'll have to make compromises in either your stream quality, resolution, or in-game framerate. An i5 should be enough to get you 30fps-720p downscale resolution stream with passable quality.
