Home Button

Try force restarting your iphone

https://support.apple.com/en-ca/guide/iphone/iph8903c3ee6/ios

Or you can try updating again through a PC or Mac

https://support.apple.com/en-ca/HT204204

If the problem persists contact apple support here:

https://support.apple.com/en-ca/contact

You can try using assistive touch or look for an app that can give you a virtual home button. You can also try doing the update via your computer.

I advise you to visit here -- Did a quick Google search on the problem, sounds common among iPhones w/ iOS 11/12/13 updates --

Wow, what an answer? You do realize the iPhone 5 can't run anything past iOS 10?

Tell me more. I’m learning something new everyday.

They can't do a forced restart if the home button doesn't work, and they can't update for the same reason.