Random thoughts:
Price better be good, what with Miles and De-Lam
Is your 5300 Pound Trailer a Guess Weight or a Scale Weight? Stuff always weighs more than we guess.
You should be able to de-code that Door Sticker and determine which Axle Ratio and Transmission it has.
Should be a sticker inside a Cabinet saying what it weighs as built. How much "stuff" will you have aboard? Your Hitch has a rating, and you can upgrade that. Might also have to upgrade the Frame. The controlling spec is Gross COMBINED Vehicle Weight Rating/GCWR and at the moment we don't have that number. We have the Gross Vehicle Weight Rating/GVWR and "max trailer" is GCWR minus GVWR. If your loaded Class C is Under GVWR, you can tow a little more before you reach GCWR.
You're probably doing this on a budget like most of us. If you weren't you'd be talking about your F450 Diesel and Gooseneck Horse/Bunkhouse Trailer. So...
What rigs do you see at Shows? I'd venture this 19G is about like an F250 V8 Gasser with a Truck Camper.
IMICHABOD posted stickers from a 2010. Using that, I found
this spec sheet. It indicates the Transmission is that good 5R110, and the brakes (at least in front) are as big as an E450. Looking for a GCWR. No joy so far.
Only way I'm not saying No Way, is your notation of "Midwest." The combination will be marginal, but you might get away with it on flat land. I'd like to know actual scale weight of RV and Trailer and Loading. I trust you have braking on the trailer.
Midwest is Flat but it's HOT, so if I was planning to use this RV with the horse trailer and tow 300 miles, would upgrade the transmission cooler, and change rear axle lube to full synthetic.
EDIT: Found
this sheet for 2013. It suggests you could go close to 7000 pounds, but that's usually based on a GCWR, meaning an empty van with just a driver could tow that 7000, reduced by passengers and cargo in the van.