iPhone 4s endless flashing Apple logo, restore not possible error 4005

First Joy, follow this article to resolve or find a path to resolution regarding the error you're getting in iTunes.

iOS: Restore errors 4005, 4013, and 4014 - Apple Support

If you can get past that error, you're on the right track restoring the operating system. Just remember to set up as new and test without your backup folder first. If the issue persists when it's set up as new, you could have a hardware failure on your hands. If the device works fine, but acts up when you restore your backup, then you have the problem isolated to being a corrupt backup. If the problem is still gone after you restore your backup, then it was an iOS failure.

Good luck!!!

Well, you must try to restore device using at least two different USB cables and two different PC. Besides, must have the latest version of iTunes.

If the issue still persist then contact to Apple Support. Apple will send you RTA upon 4005 error code.