i cant start my iphone 5s

Sounds like the battery is run down. Have you plugged the device in to charge it. First you say you cannot start the device, then you say when you start it, something occurs. So that sounds like you can start it. If you plug the device in for about 30 minutes, if the device does not start on its own, while still plugged in, hold the sleep/wake and home buttons together until you see the Apple logo and then release. The phone should restart.

Okay. Your choice.

Thanks a lot ChrisJ4203, I thought my iphone was "kaput", since it did not start at all even when it was plugged; the holding of the two buttons at the same time it worked🙂

See this support document for an error 4013. iOS: Restore errors 4005, 4013, and 4014 - Apple Support

That can be a tough one to deal with. You are probably just as well off to take the device to Apple, as that is the final step for that particular error.

you save my life brother thank u so much 🙂