Is rooting the Samsung Galaxy S5 G900V impossible?
I understand that you cannot root your phone the normal way, because Verizon won't let you unlock your bootloader. I believe Kingroot should work. It was able to successfully root my Samsung Galaxy S3 running 4.4.4. If that doesn't work I would try Kingoroot. Hope this helps. We all hate Verizon for keeping our bootloaders locked.

If those don't work, I would suggest finding a Carrier unlocked phone. When you go to Verizon to get it hooked up, make sure familybase is disabled, or they won't be able to hook it up. I recently was able to hook up an unlocked Nexus 6p (great phone).

Good luck!