No, your AT&T phone doesn't have 5G yet
https://www.cnet.com/news/no-your-at-t-phone-doesnt-have-5g-yet/
The only thing is that 5G E isn't actually 5G. AT&T's 5G Evolution technology is really just advanced 4G LTE with some confusing marketing language. It's supposed to set the foundation, so AT&T can eventually roll out 5G, but it's still 4G technology.
An AT&T spokesperson reportedly told FierceWireless that the company will "roll this out on a handful of devices, with more devices showing the indicator in spring 2019."