Below is an article from a Redditor named iPhonekid in which he teaches you how to use Verizon iPhone 5s on ATT’s LTE network and he provides an image proof too. For images go to below imgur link.
How-to: Verizon iPhone 5S on AT&T
Here are all the steps I took, some might be unnecessary but they should work for you
1.If upgrading from an iPhone 4 to an iPhone 5 or 5S, you need to call AT&T (or
visit a store) and have them change your unlimited data plan to an unlimited 4G
LTE data plan. You will also need to go to an AT&T store and acquire a new LTE
2.After installing the new sim you will notice that you still only receive AT&T 4G
3.Hit create APN. Select AT&T LTE as your carrier. Hit the gray Create APN and
5.You should now be connected to AT&T LTE but if you try to open up Safari you
will receive this error “Could not activate cellular data network. You are not
subscribed to a cellular data service.” (see imgur album below)
6.Reset your Network Settings. This will, again, restart your phone.You’ll attempt to
open up Safari and will receive the same error. Go to Settings -> General ->
Profiles. Remove the Unlockit APN profile.
7.Restart your phone one last time and you will notice that you are still connected to
AT&T LTE, Open up Safari and your web pages should now load. MMS