Transfer music, notes, photos, contacts, SMS and more from one Apple device to another. Follow these steps:
Step 1: Make sure you have the latest version of iTunes and iOS.
Step 2: Connect your current iPhone to iTunes and sync it. Verify that your original iPhone is backed up. For more information on how to do this, see iPhone: iPhone and iPod touch: About backups
Step 3: Connect your new iPhone 5 to iTunes (on the same computer you used to back up your current iPhone 3G).
Step 4: iTunes will ask you if you want to restore from a backup or set up your new iPhone as a new phone. When prompted, select the backup of your current iPhone. If iTunes does not prompt you to select a backup to restore when you connect your new iPhone, use iTunes to restore iOS on your new iPhone and try this step again. Note: During the process of restoring your old backup to a new iPhone, you may see the iTunes progress bar pause. If this occurs, please allow for additional time for the upgrade to complete.
Step 5: After iTunes finishes restoring the backup you selected to your new iPhone, the iPhone will restart.
Step 6: When your new iPhone appears again in the iTunes window, select it.
Step 7: Click the tabs (Info, Music, Photos, and so on) and verify or change the items you want to sync.
Step 8: Click Apply to sync your new iPhone 5 with iTunes.
Step 9: Verify that your saved contacts are present on your new iPhone.