This is a topic covered in
the guide (though it is a section that requires a little bit of an update), along with a lot of other useful and relevant information.
If your 4S is carrier unlocked for international use, you can either take it to Truphone or to either Verizon-based MVNOs Page Plus or Selectel. (This said, Truphone is more of a hardcore minimalist service option for someone looking to go with a PAYGO plan to begin with.)
The Verizon branded 5's GSM/LTE SIM slot is already carrier unlocked for domestic GSM networks, so you can take it to any AT&T or T-Mobile based MVNO, or you should be able to take it to Page Plus with the purchase of a PP LTE SIM card and a commitment to at least their $30/month plan. Selectel is not currently set up for LTE support. If you do want to take it to Selectel or to use one of Page Plus' cheaper plans, it rapidly gets more technical and complex as you'll need to flash the handset to only use 3G data connectivity, and even then you may have trouble activating at this point.
If you're going to waste your time, money and resources replacing like for like handsets to use a different carrier, don't bother keeping yourself locked into a CDMA network and jumping from Verizon to Sprint (even if there's still Verizon roaming as is the case with Ting), as Sprint MVNOs can only activate Sprint branded handsets. You'll have far greater coverage and flexibility either staying with a Verizon MVNO or going GSM if you have the network coverage. Your iPhone 5 is already in the sweet spot for that level of flexibility, so keep it, because needlessly switching to a Sprint iPhone 5 to use Ting will strip you of the option to go with a GSM carrier and not give you any better network footprint.