Tundra Crewmax shortbed pull a 5th wheel?

Have you looked at the pin weight on that 5er? NADA list the GVWR as around 8000 lbs which is light, but on most 5er's the pinweight is around 20%, which would be about 1200 lbs empty. Your truck I think has roughly 1500 payload so by the time you get in the truck, and add a hitch setup with it otherwise empty your right up at the payload capacity.
The truck will pull it, but she will likely be over the payload limit.