New to RV and buy my first RV

[CWSWine]

The truck is a 2012 Silverado 1500 4WD Ext Cab LTZ
Vortec 5.3L V8
6 Speed Auto
Z85 Handling Trailering Suspension
Heavy Duty Trailering Equipment
GVW Rating 7000 LBS
Rear Axle 3.42 Ratio
My owner’s manual says:
5.3L HD Cooling Pkg Fifth Wheel Trailer with 3.42 Axle
Maximum Trailer Weight = 9600 Lbs
GCWR = 15,000 Lbs
The Trailer:
Standard pull style trailer 24 foot with a factory weight of 5272 lbs and a Max cargo weight of 1728 lbs for a total of 7000 lbs even. These numbers come off the yellow stickers on the door. Would this Trailer be a good fit for my truck.

[anaro]

The weak link on a 1/2 ton tends to be payload. Go look at your drivers side door jam and look at the tire loading sticker where it will say "occupants and cargo should not exceed x lbs". Now subtract the weight of everyone and everything that will be in the truck when towing. that new number is your available payload. the loaded Tongue weight must be less than this number. loaded tongue weight should be 13-15% of loaded TT weight. An even more accurate way to approach that is to go weigh your truck loaded ready to tow with all passengers, pets and gear that will be in it when towing plus a full tank of fuel. Take the scaled weight and subtract it from TV gvwr to get available payload. Take the scaled weight and subtract it from gcwr to get adjusted towing capacity. You need to stay within all these weights.

The TT you list, gives a 5272 lb dry weight and a gvwr of 7000 lbs. Most tend to add 1000-1500 lbs to their TT. Some mee, some less. With that low of a cargo capacity, I would do your calculations using the TT gvwr. For 7000 lbs you are looking at a potential tongue weight of 910-1050 lbs.