Q: My iphone 5 internet and 3G is not working

Hey Marykins89,

Sounds like you've already done some parts of the troubleshooting process, but there are still a few more steps you could take to try and resolve the issue:

1. Toggle airplane mode: Tap Settings, turn airplane mode on, wait three seconds, and then turn off again.
2. Restart your iPhone.
3. Ensure that your software is up to date:
   • Check for a Carrier Settings Update. Tap Settings > General > About.
   • Check for an iOS Software Update. Tap Settings > General > Software Update.
     Note: Some updates may require a Wi-Fi connection.
4. Remove the SIM Card and reinsert it. Allow the iPhone to acquire the network again.
5. If your SIM card has SIM PIN enabled, try toggling it off: Tap Settings > Phone > SIM PIN.
6. Try another location. If a different location works, but the original location still does not, contact your carrier to report the issue.
7. Reset network settings: Tap Settings > General > Reset > Reset Network Settings.
8. Restore the iPhone as new.
9. Contact your carrier to:
   • Verify that the iPhone is properly set up on the account with the appropriate, current data plan.
   • Verify that there are no account-related blocks.
   • Find out if there are specific error messages in the carrier logs that could help determine why the issue is occurring.

If none of the above steps resolves the issue, contact your carrier, make an appointment at an Apple Retail Store, or contact AppleCare to troubleshoot further.

via: iPhone: Troubleshooting a cellular data connection

http://support.apple.com/kb/TS3780

Regards,

Delgadoh