Here's how you can transfer to iphone 5 with iTunes:
1.Back up your old device using iTunes and transfer your data from your device to your computer.
2. If your device uses a SIM card: Use the SIM-extractor tool or a paper clip to remove the SIM from your old device and insert it into your new device. If your carrier provided you with a new SIM card, use that instead.
3. Turn on your new device and complete the Setup Assistant by selecting your language and country, and choose whether to enable Location Services. When prompted, choose your Wi-Fi network.If you don’t have a Wi-Fi connection, you can also activate by tapping "Connect to iTunes".
4. When prompted to set up your device, select "Restore from iTunes Backup".
5. Connect your new device to iTunes (on the same computer you used to back up your current iPhone). iTunes will ask you to restore from backup or set up as new. Select the backup of your old device and choose Continue.
6. When the restore process is complete, your device will restart. Then it will be ready for use. You should keep your device connected to iTunes to sync data not contained in the backup (such as music, videos, apps, and so on). You can verify and change which data are synced by clicking the syncing tabs in iTunes.
You can also use iCloud to transfer information from old iPhone to new iphone 5, here's an article from Apple's Support:
http://support.apple.com/kb/HT2109