Have a 6k pound RV.
Had an '01 w/ 7.3.
Have a Tundra w/ 5.7.
Will it do it? Yeah.
With ease? Depends on your definition.
If your truck has a chip or programmer, you may like it a little better.
If not, you may like the Tundra better.
Having owned both, the Ford was loud, rattled my teeth and bruised my kidneys.
The Tundra is quiet, smooth and way more comfortable of a vehicle to drive. The 5.7 is a pretty strong motor.
But if you have to be first up the mountain, and are looking to upgrade, you may consider an '11+ Ford with the 6.7 and coil over suspension.
Did I mention the Tundra is quieter and smoother?