my iphone 5s does not have the wi-fi calling feature

You do not say who your carrier is. Check out this support document to see what carriers are capable of Wi-Fi calling and other things you may have to do. Make a call with Wi-Fi Calling - Apple Support

I have AT&T LTE and have verified they support Wifi calling. I have the updated IOS. The Wifi calling option doesn't even appear under settings/phone in my iPhone 5s. Any idea why this is? Thanks.

Did you verify that AT&T supports WiFi calling on that model phone. If I recall correctly, my carrier doesn't.

Thank you. The support documentation I have been able to find on the net, as well as a call with an AT&T representative (who frankly did not sound knowledgeable on the topic, both say the 5s (actually the 5c and forward) are supported by AT&T. I'm concluding however, that at least in some areas, that is not the case, and that the support actually starts with the 6.

You might try calling AT&T back to get a different rep.

I looked for this today, too.

This page seems to give the negative answer:

https://forums.att.com/t5/Account-Features/Wifi-calling-on-iPhone-5S/m-p/4325429 #M21560