Resolve iOS update and restore errors in iTunes - Apple Support
If you are still unable to restore, you may find this article useful as well:
If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support
Error 53 based on the information that I've gathered is a hardware issue that stems from Touch ID.
The recurring theme between the reports seems to be replacement of the screen or the home button.
When a home button is replaced with a button from a different the device it causes an issue with the Touch ID functionality leading to error 53.
What I would recommend doing is calling apple support and going over some troubleshooting steps with them.
If a backup / restore does not resolve the issue then take the device in for service or mail it in.
Something like this should not be considered accidental damage so it should be free.
Now if you're out of warranty then you're out of luck as with any manufacturer.