Straighttalk does the "Bring Your Own Phone" option. They also do allow the iPhone 5 on their networks. However your question would be more geared to Straighttalk themselves because they will be able to give you a for sure you can use it or you can't.
On Straight Talk's BYOD plan, you are to dial *#06# on your phone to give you your MEID/IMEI/ESN number to type in on their website. Afterwards they should tell you whether your phone will work on their plans or not. You won't know for sure until after you have purchased the SIM card and refill card. Because the iPhone 5 on Verizon is CDMA, I doubt it will work on straight talk since it requires a SIM card to activate their GSM iPhone models.
Well maybe I should just make a fresh start with a new carrier.I'm lucky to get 3g at my house and 4g was what I signed up for-my friend has a straight talk phone that works great at my house for 1/2 the cost of my verizon plan.