Grocery getter? Seriously? There are plenty of RVs available that will comfortably handle.
Payload is generally your limit for RVing, then maybe receiver limit. Some half tons have 3000 pounds of payload, some have 800. Most -13 crew cab 4WD GMs are in the 1400 pound range, and 14+ are more like 1650. A 9000 pound loaded travel trailer will have about 1100 pounds of tongue weight, maybe as high as 1350. I have seen some half ton pickups with far less than that, and you don't have anyone in the cab yet. 5th wheel is worse. A 9000 pound loaded 5er will have 1350-2250 pounds of pin weight, plus 200 pounds for the receiver in the bed, plus people in the cab. So generally, 5th wheel does not work out favorably for half tons.
Open your driver's door and locate this sticker. Note what your truck has where this says 2051. subtract the estimated weight of family and a couple hundred more for the bed full of camping gear. Multiple by 7.7 for loaded trailer weight. Typical weekend RVers add 1000 pounds of stuff to the RV dry weight. Clothes, food, eating and cooking supplies, games, toys, etc. IT all ads up, so subtract 1000 pounds from your last number. That's a good dry estimate.
I'll assume you have a 2013/2014 truck, 5.3L, 6-spd trans. That's plenty of gearing with 3.42 and most RVers are happy towing about 7000 pounds loaded. Stick to about 6k dry, use a weight distributing hitch with integrated sway control, and you should be pleased.