Iphone 5 error 4005

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iOS System Recovery Guide How to Fix with Various iOS System Issues

This article may help you. It is for iPhone, but the same operating system runs on iPad as well.

Several months ago I downloaded iOS 7 beta with developer program. It worked fine. When iOS 7 had officially came out, I checked my phone and it restarted on its own. The locked screen said"Activation Error: This device is not registered as part of the iPhone Developer Program. If you are a member of the iPhone Developer Program, please register your device in the iPhone Developer Program Portal at http://developer.apple.com/iphone." I went to the link using my computer, although I am not a developer, and it didn't help me.
Recent days we see lots of iPhone users reported iOS 7 activation error. How did this happened? It is probably because users installed iOS 7 beta 6. As the iOS 7 beta has expired on October 6, which means anyone still running one won't be able to use their iPhone, iPod touch, or iPad, and won't even be able to get past Activation if they try.
If you're experiencing an iOS 7 activation error on your iPhone/other device and were previously using iOS7 beta, there's a good chance to fix it with following simple steps:
1) make sure you have upgraded to iTunes 11.1.1. It is the most recent version of iTunes.
2) Plug you iPhone/iDevice into your computer. Back up the data on the device.
3) Click "Restore" on your device's page in iTunes. If this doesn't work, proceed to DFU mode
4) your device is done restoring and activating you can restore your data from your iTunes backup
5) you can use your non-beta iOS 7
If iTunes says there is no newer version to upgrade to, you can put your iPhone or device to DFU mode after the backup. DFU (Device Firmware Update) mode will make sure you download and install the latest release version of iOS off of Apple's servers.
1) Plug your iPhone, iPod touch, or iPad into your Mac or Windows PC and make sure iTunes is running.
2) Hold down both the Sleep Button (on top of your device) and the Home Button (on the front underneath the screen).
3) Keep them both held down from about 10 seconds. (If you see the Apple logo, you've held them too long and will need to start again.)
4) Let go of the Sleep Button but keep holding the Home Button for about 5 seconds. (If you see the "Plus into iTunes" screen than you held it too long and will need to start again.)
5) Restore the device

If the ios 5 is in beta. That means that it's in Test mode. If it keeps messing up and dying. It's not ready yet.

Beta = Test

So the best you can do is offer feedback to Apple over it, then restore your phone back the the latest ios 4 for the time being, and wait for ios 5 to get out of Beta mode