Apple’s official statement says, You could see Error (53) when you update or restore your iPhone or iPad (iOS device) in iTunes. Error 53 appears when a device fails a Touch ID security test. Error 53 is an unfixable error code.
After you try to update or restore your iOS device in iTunes on your Mac or PC, you might see error 53 in iTunes and “Connect to iTunes” on your device. Error 53 appears when a device fails a security test. This test was designed to check whether Touch ID works properly before the device leaves the factory, and wasn’t intended to affect customers.
How to fix my iPhone if it gets an Error 53?
Apple has released an update in iOS 9.3 to fix this issue. Follow the the steps here published by Apple to restore and recover your device from error 53.