Which is better for towing a trailer Class A or C motorhome

Think also about the total length of the two rigs and this is a factor when merging, passing, and pulling into a gas station or a campsite. A 5,000 lb. trailer load is not a big deal. Most Class C are built on a 450 or 550 frame that is plenty strong enough with the right hitch.

With a Class A I would need to tow a smaller vehicle and a trailer with whatever else. With the Class C I could get buy without the second vehicle in tow.

Don't forget the Super C's! Plenty of towing capacity and power :-)

In general, a Class A will do better pulling a trailer but there are a lot of variables. How much can the RV tow? How good is the hitch? How long is the wheel base? A shorter wheel base will cause the RV to move when the trailer is pushed sideways. A longer wheel base will be more stable.

we had a class C while towing our 24' cargo trailer, and our Class A beats the heck out of it. A diesel pusher....niiiice :)

I see mostly class A towing cargo trailers with any significant size on the highways. Class A will usually have a heaver and more stable chassis...get one with 22.5 wheels will make a very significant difference.

Either will tow a trailer up to the limits of their rating without much trouble.
Quite often a Class C will have a hitch rating of 3500 lbs. This rating MAY be increased by strengthening the frame extensions and the hitch, IF you can find a shop that does such work on a regular basis for trucks. There are such shops out there. The limits based on engine power and/or transmission life are much more difficult to change, but it can be done.
Class A motorhomes typically (but not always) have a hitch capacity of 5000 lbs. This, too, can be changed by reinforcing where needed.
Many Diesel Pusher motorhomes have a hitch capacity of 10,000 lbs.
It is very likely you will have to install a brake controller in the motorhome. Not many people tow trailers with them, so a brake controller isn't often installed. Of course, you could get a trailer with surge brakes which would take care of the problem.