Q: iPhone 5 constantly stuck in a rebooting phase?

So I decided to see if my iPhone would start today, after forgetting about it for awhile. While I was at college it would have this habit of showing like the customary low battery screen, then go to the white Apple screen for a few seconds, and then do that process non-stop. I would leave it in to charge for like days on end and it would never turn on. Today, I decided to try to see if I could fix that. I looked online and saw different ways like taking out the SIM card(which I tried multiple times), and the usual recovery mode for a phone. I held both the power and home button for 10 seconds, and then the home for 15 more when it showed the iTunes logo on the screen. I plugged it into my computer (there's nothing wrong with my computer, it's a mid-2015 MacBook Pro on the latest iTunes), and it showed that my iPhone needed a software update so I downloaded the software. After it downloaded, I pressed the "Restore and Update button", and let it do its thing. However, when it got to the "Waiting for iPhone" bar, it shows up "The iPhone iPhone could not be restored. An unknown error occurred (2001). I have tried to reset it and factory reset it several times, and now as it is plugged into my MacBook, it just shows the connect to iTunes screen, and as soon as I unplug it, the screen turns blank. Any help?