Check out your Tundra as to what it has on it. Engine, axle, tow package etc. Then look up your tow capacity and as others have mentioned, load capacity. I have worked in campgrounds where 5ers were pulled successfully with a fully decked out Tundra. I have no issue towing my 27RLS with my Tundra, and I typically pull in Colorado. Mountains are a non issue.
Quick answer... Maybe