iPhone 5S unlock question
Most likely the phone will work, but you'll have to borrow an IMEI from the Verizon sequence assigned by Apple. With the right SIM and an activation run with the wrong IMEI (but a Verizon iPhone one), you should work.
One can not buy any random iphone and activate it on Verizon's network. It needs be a CDMA iphone. So GSM handsets (AT&T and T-Mobile) are out. Even though Verizon and Sprint use the same technology...they don't broadcast on ALL the same frequencies. SOME but not ALL. Then there is the question of the CDMA portion of the phone likely being locked to the carrier's own network as well as preferred roaming lists. You may want your phone to choose whichever signal is strongest regardless of network but Verizon wants your phone to choose its network over Sprint's because they would prefer not to pay Sprint a roamIng fee for you straying onto...