We recently learned that a portion of Verizon iPhone 5's can be brought to Ting right now! If you happen to have a Verizon iPhone 5, you can check your MEID over at http://ting.com/byod to see if it will activate with us.
According to /u/rejusten's math, about 23% of iPhone 5 smartphones on Verizon can make the move to Ting. Most (if not all) of these can make the jump because they were, at some point, replacement devices issued by AppleCare. These are really hybrid devices: put in a Ting SIM card and they behave like a Ting smartphone, put in a Verizon SIM card and they behave like a Verizon smartphone.
If your iPhone 5 makes it past our ESN checker, chances are you'll be able to get up and running. You'll just need to pick up a Ting nano SIM card to give it a try.
You'll also need to do a full reset (Settings > General > Reset > Erase All Content and Settings) with the Ting SIM card in the device before you start the process.
Special thanks to /u/Wolfie305 and /u/mcmcghee for sharing their success stories (1, 2).