iphone 5 can not send out sms

Talk to your carrier. It's their issue.

What you have to do is a clean restore inside of iTunes. A backup is required just so your iPhone isn't erased.

iTunes: Restoring iOS software

http://support.apple.com/kb/HT1414

iOS: How to back up

http://support.apple.com/kb/HT1766

If the problem still happens, you need to setup your iPhone as a new device.

iOS: How to back up your data and set up as a new device

http://support.apple.com/kb/HT4137

One of these will solve your issue.

You did a full restore and restored your backup, and the problem still happened?

Then restored, did not put your backup back on, and had a factory fresh, unmodified phone, and the problem still happened?

If that's the case, you need to contact your carrier, it's not an iPhone issue.

Howpg wrote:

done all the things as you proposed , still can not send sms, but it can send sms on other iphone5, therefore not the provider/carrier problems

If the problem was the iPhone hardware, you'd have no service at all or something similar. There isn't an "SMS Chip" inside the iPhone that is only half working. There is a software problem. And the steps above should have solved that software problem. If you still have a problem, I recommend giving Apple Support a call to troubleshoot why this still isn't working and then to make sure all the right steps were done.

Hi Friend,

Be sure you turn on the carrier's network. Check it in: Settings>>Mobile, and then turn on Cellular Data, Active 3G and Roaming.

You also must to set the Mobile Data networking according your carrier's plan, fill the blanks like MMSC, Proxy MMS and MMS size.

Hope it will be helpful