Is there a way to enable wifi-calling on an iPhone 5 Yes, I know that both Apple and my service provider say minimum iPhone 5c.

However, the 4 and 5 can do facetime, skype, etc, so shoving bits over the air isn't the issue.

Can this functionality be enabled through a 3rd party app and/or jailbreaking?
I used Talkatone on my 5S while out of the country, and it worked pretty well. http://www.talkatone.com/

This is a 3rd-party app that will assign you a new number, so it won't "enable" WiFi Calling on your phone using your existing phone number. 

While FaceTime and Skype do work, WiFi Calling is slightly different. It involves the phone connecting to your carrier's servers through the internet, which for some reason isn't supported on certain devices (especially odd since my 5S is supposed to have WiFi Calling, but AT&amp;T chooses not to support it).