Yes and no.
You can get a good i5 cpu with 16gb ram and modern motherboard. A case is cheap, and a bit of cooling and you're $350 to $500. What you are missing is the GPU. This is what will kill it for gaming though. You need to figure out what type of games you want to play "at most", and that's together with the budget the limit. A nice 1080 or 2080ti will do just fine for a lot of games. Integrated graphics: skip it.. What comes with the i5 is fine until you can get your hands on a nice gpu deal. But it will drive it over 500
