Will a unlocked sprint iphone 5 work on verizon?

My girl friend is due for an upgrade on her sprint and i wanted to know if we can get the iphone 5 have sprint unlock it and use it on my verizon, is that possible?

Yes it will.
both networks are CDMA to begin with

The phone must be flashed to Verizon, unlocking the phone has nothing to do with it as Verizon is CDMA like Sprint.