It would be exceptional for a 2005 Class C towing to have a tow limit of greater than 3500 lbs, which part of the reason we ended up with a Class A. Better check the manual.
Also, just because the hitch says 5000 lbs doesn't mean the chassis can handle it. They have to put extensions on the frame and they may be limited to 3500 lbs.
The V10 can handle the weight, the F53 Class A's don't have a problem with it. The issue is the strength of the chassis and frame extensions.
2002 35R Southwind, W22 8.1L Vortec UltraPower, 19.5' wheels
Toad: Wrangler, lifted and on 35" tires