I'm trying to unlock my iphone5 (approved by ATT), and I have backed-up-restored. How do I know it is unlocked succesfully

The process includes restoring the iPhone as new. When you do that, you should get a Congratulations your iPhone is unlocked message.

You are probably hitting Restore Backup. You need to hit Restore iPhone...

Also, just so we are clear, the Apple unlocking instructions state that you only have to restore if you do not already have another carriers SIM that you want to use in the phone.

The restore process is only intended for if you do not have another carriers Sim and you want to make sure that the phone is unlocked.

This process is for the iPhone 5 and forward.

If you have a SIM card from a carrier other than your current carrier, follow these steps:

1. Remove your SIM card and insert the new SIM card.
2. Complete the setup process.

If you don't have another SIM card you can use, follow these steps to complete the process:

1. Back up your iPhone.
2. When you have a backup, erase your iPhone.
3. Restore your iPhone from the backup you just made.