Q: iphone 5s error code 4013

Resolve iOS update and restore errors - Apple Support

Before You Start

http://www.igeeksblog.com/how-to-fix-itunes-error-4014-4013/

As always:

• Use the latest version of iTunes
• Make sure iPhone has enough space to bring in a new update. A gig or more is recommended.
• Also make sure the iPhone is not low on battery.

The Real Problem
Error 4014 (or 4013) is usually associated with a hardware problem – a faulty cable, a faulty port etc. On the surface, your iPhone connects to the computer, iTunes recognizes the device but somewhere down the line, iTunes thinks that the cable is not really that good. Or may be the port isn’t.The first thing you try should be change the USB port to which you connect the iPhone. Next up, change the cable that you use. Arguably, this has worked not for everyone but for a few people.
As an extreme measure, you can also try updating from some other computer which has the latest iTunes installed.
Backing Up and Going Into Recovery ModeIf you are trying to update the firmware without doing a clean restore but running into this error (even after changing the cables), it’s time to cut the chase. This method is usually recommended as the last-thing-to-try but I think it’s easier to get this done with right away.

• Connect your iPhone to the computer. Fire up iTunes.
• Backup your iPhone.
• Now disconnect the iPhone, quit iTunes.
• Put the iPhone in recovery mode. The short version goes like this: press and hold power and home buttons till the screen goes blank.
• Open iTunes on PC.
• Connect the iPhone. iTunes should indicate (through a dialog box) that an iPhone is detected in recovery mode.
• Now go ahead and restore the device as new. This will erase everything but you will have the backup to restore from.
  

Some Notes

• Occasionally, the error seems to vanish when people update to the last iOS 6.x version and then update to iOS 7. (This applies when you are on iOS 6.0, 6.1).
• Clear out apps and app memory to free up space on your iPhone. Although this sounds very unrelated to this error, it has helped.

darrinfromwooster wrote:

 

I have tried all that. My phone is stuck on the connect to itunes screen.

iOS: Restore errors 4005, 4013, and 4014 - Apple Support  Per the link I provided, what did Apple Support say when you contact them about the issue?

Since you stated you've tried all of that.