AT&T doesn't support your device for Wifi calling.
iPhone 6 and newer iphones only.
AT&T has, since the inception of wifi calling, only supported it on iPhone 6 and newer iPhones (so 6, 6s, SE, iphone 7 and 7 Plus only at this time). They have never supported or enabled it for iPhones older than the iPhone 6.
So while the iPhone 5S as a device supports the feature, AT&T has never supported it on that device. They are able to pick and choose which devices they enable the feature with on their network.