To my understanding, you cannot use an AT&T iPhone 5 on the Verizon network. Verizon uses a CDMA network and AT&T is on GSM. AT&T iPhones bought through subsidy are (normally) locked until the completion or termination of the user's contract.
If you had a Verizon iPhone 5, however, you could use it on the AT&T network, with exception to LTE connection. The plus side of a Verizon ip5 is that it is unlocked out of the box.