To make a long story short, I took my iPhone 5 apart in order to change the battery (which you're not supposed to do, but I don't think Apple does iPhone 5 battery replacements anymore so I didn't have much of a choice), and when I put it back together it had all sorts of problems (mostly stuff relating to the iOS... it was stuck in Recovery Mode for quite some time...)
But the biggest problem (now that I've managed to get it out of Recovery Mode) is that the buttons no longer work. (The power button as well as the home button no longer work. I'm not sure about the volume buttons, but I'm guessing they don't work either.) I don't think I damaged the hardware when taking it apart, though I suppose it's possible.
I'm just wondering if this has happened to anyone else, or if anyone knows how to fix it?
I did try the "software workaround" on this page : https://www.macworld.co.uk/how-to/iphone/how-fix-broken-iphone-home-button-3463402/ , and it works, but it's far from ideal. Without the power button working, there's no way to power off the phone (or even turn the screen off). And I really don't want to leave the phone on all the time.
(I'm now using an Android, but I'd like to get the iPhone working again.)
Sounds like a hardware issue. Probably didn't get something seated properly or otherwise squished some wires or components.
Redo the process following this guide:
https://www.ifixit.com/Guide/How+to+replace+your+iPhone+5+battery/10587
See if that changes anything. Don't forget to drain battery before opening the case.