Randy, welcome to iRV2.
As wallynm says, make sure you have enough GCVWR to handle the weight of the Tahoe AND that your hitch is rated high enough. Many hitches are rated for 5,000 lbs and, although 5,300 isn't that much overweight, you also have to remember that rust and age may have weakened things so you don't want to push too far. Also remember that the published figures for curb weight are dry weights. Fuel, oil, water, optional equipment, and personal items can add several hundred lbs to the weight of your toad. You might be able to replace your hitch with one rated higher, but the motorhome frame probably isn't rated for the higher capacity hitch.
Also, even though your diesel will have more torque than a gas engine, 275 hp sounds like it might struggle a little. We towed a Silverado extended cab 4x4 (probably about 5,200 lb with full gas, small tool box, and miscellaneous items on board) behind our gasser (340 hp) for a year and it was sort of OK, but we didn't take it over any big mountains either.
2015 DRV Tradition 375KPS
2015 Chevy Duramax 3500HD LTZ Dually
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