my mistake. i misread. I would honestly go to an AT&T store and complain about it. they can try a new sim card (yes thats actually worked for me before). Also they'll have other 5Ses in the store that will hopefully show LTE while urs show 4G so u can prove something is up.
a) I have been through 3 sim cards and 4 iPhone 5s, and was able to replicate the issue on all combinations. I still have my iPhone 5 and it works fine on LTE with the SIM card that doesn't work well on the 5s
b) Going into the AT&T store to talk about an issue like that is like going into a McDonalds and discussing the culinary technology behind their food with the guy frying the fries. It's not productive for me, nor them. Same with AT&T. There is nothing gained by going to the store. They don't even effectively communicate up to corporate, because as with any retail, the corporate office doesn't take much seriously that comes from a retail store. Just a bunch of uneducated, unskilled labor.