re: iPhone 5 contacts won't snyc
your contacts wont sync through iCloud? when you do a sync in iTunes? you have to be more specific about how you are syncing them.
If it is iCloud check your iPhone under Settings, iCloud and make sure you are logged into your iCloud account and Contacts is toggled on. If it is logged in try exiting the contacts app in multi-tasking. Then turn off Contacts in Settings, iCloud it will ask whether you want to delete the contacts from your phone or keep them. I would suggest using "Keep them" unless you are absolutely certain they are in iCloud. Then reboot the phone and turn Contacts back on check if they sync.