Can I use the Sprint / Verizon iPhone 5 (A1429) on AT&T's LTE network?

No. The iPhone 5 comes in 3 different versions, designed to work with different LTE radio frequencies around the globe.

The CDMA iPhone 5 (otherwise known as A1429) is designed for CDMA carriers including Sprint and Verizon. This model will be compatible with some GSM networks internationally, however the device will not be compatible with AT&T's LTE network.