iPhone 5 still has previous owners itunes info
Have you tried this?


  Settings > General > Reset > Erase All Content and Settings
  (c.f. http://support.apple.com/en-ca/HT4137#erase your device)


If you cannot erase this way, Apple says (down a bit on that page) that you ought to restore using iTunes, which won't be helpful without the original owner's iTunes backup.

If the device is locked via "Find My iPhone Activation Lock", then you'll need to go through this process:


  http://support.apple.com/en-ca/HT201441


which requires the previous owner to log into their iCloud account, at http://www.icloud.com/find , then click on the device they sold you, then "Remove From Account".

In general, its a good idea to have the previous owner go through these steps as they're selling the device to you:


  http://support.apple.com/en-ca/HT201351


Good luck with this!