That is correct - for Texas (and Florida). However, other states may be different. For example, if you (as a Texas resident) want to drive a motorhome over 26,000# you must have a Class B license (car type = class C). If you (as a Florida resident) want to drive a 42,000# motorhome all you need is a regular (class E = car type) drivers license. One of the reasons retirees move to Florida. I have not looked into whether a 5th wheel RV trailer is exempt.
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In Texas:
3. Class C driver license permits a person to drive the following vehicles,
except a motorcycle or moped:
a. a single unit vehicle, or combination of vehicles, that is not a Class A
or B; and
b. a single unit vehicle with a gross vehicle weight rating of less than
26,001 pounds, towing a trailer not to exceed 10,000 pounds gross vehicle weight rating or a farm trailer with a gross vehicle weight rating that
does not exceed 20,000 pounds.
http://www.txdps.state.tx.us/DriverLicense/documents/DL-7.pdf
In Florida a Class E license is what most people have:
NonCommercial Driver Licenses
CLASS E: Any non-commercial motor vehicles with Gross Vehicle Weight Rating (GVWR) less than 26,001 pounds, including passenger cars, 15 passenger vans including the driver, trucks or recreational vehicles and two or three wheel motor vehicles 50 cc or less, such as mopeds or small scooters. (see below). Farmers and drivers of authorized emergency vehicles who are exempt from obtaining a commercial driver license must obtain a Class E license.
Official Website Florida Department of Highway Safety and Motor Vehicles
But an exemption allows someone with a 42,000# motorhome to drive it with a class E license.
Exemption Means the following persons are not subject to the commercial driver痴 license
provisions (Florida law only, other states may differ and exemptions must be verified):
Drivers of authorized emergency vehicles;
Military personnel driving military vehicles;
Farmers transporting supplies, machinery or agricultural products to or from market or
first place of storage or processing, within 150 miles of their farm (must have a Class D
with F endorsement or a current chauffeur痴 license until it expires);
Drivers of recreational vehicles as defined in s. 320.01; and
Drivers of straight trucks as defined in s. 316.003 that are exclusively transporting their
own tangible personal property, which is not for sale.
Farmer Means a person who grows agricultural products, including horticultural products
http://www.dot.state.fl.us/mcco/downloads/policy/04-10_2008-08-08_cdl_enforcement.pdf
The only way that you can't tow over 10k with a class C in TX is if the combination is over 26k.