Q: all of sudden my iPhone 5 S turned off, I could not restore it.  The message error 40

Hello SAS1963,

This error can be indicative of hardware issues or conflicts with your security software.

Check for hardware issues

Try to restore your iOS device two more times while connected with a cable, computer, and network you know are good. Also, confirm your security software and settings are allowing communication between your device and update servers. If you still see the alert when you update or restore, contact Apple support.

Common errors: 1, 10-47, 1002, 1011, 1012, 1014, 1000-1020.

Resolve specific iTunes update and restore errors

http://support.apple.com/kb/TS3694

Cheers,

Allen