Why would the "Enable LTE" option be missing in an iPhone 5?
The LTE toggle shows up when your carrier settings indicate LTE is available for your device.

If you have data, you can update OTA by going to Settings > General > About and waiting (or tapping on your current carrier settings to see the details).

A tethered check is also available by connecting your iPhone to iTunes and checking for an updated carrier profile for your provider. If there isn't, the most likely explanation is that your provider has not enabled LTE in their carrier settings. If so, contact your provider on whether any LTE (even if not theirs) will work on your iPhone.