Towing Capacity

A Ford F-250 could be a whole lot of different trucks. 1970 model or 2016 model? 4wd, diesel, long bed, loaded with options or no options?
Is this 7,500 pounds what the trailer supposedly weighs dry or what you think it will weigh after you add all your gear and supplies?
I would say that is this is a typical loaded up 4wd crew cab diesel F-250 and the 7,500 is the dry trailer weight then you will quite likely run out of payload on the truck after you load the trailer and your large family.

Truck? Figure roughly 8000 pounds loaded ready to go if its a diesel. If a gasser, maybe 7500 pounds. With a 10,000 GVWR that would leave you 2000 pounds for hitch weight and what ever else you might pile in the bed.

I appreciate everyone's comments but I am still a little confused. I don't plan on weighing the truck before I buy it. I don't know if anyone can answer this but if I buy a Ford F-250 would it be safe to assume it could safely pull a 7500 pound trailer and my family of 5 and sometimes 6?

GCWR will not be found on the door post tag. It is usually found in the Owners Manual under "Towing".
Towing capacity is the GCWR minus the actual weight of the vehicle minus any other load on the vehicle.
Yes, you must get the vehicle weighed before you can even begin to figure this out!
So: Let's say the GCWR of your vehicle is 20,000 pounds. The vehicle weighs 8000 lbs. with full fuel and the driver. that leaves you 12,000 lbs for a trailer. But wait, you have to add the weight of your spouse, 2 or 3 kids, firewood, dog(s), etc. to the weight of the truck. That leaves you with 11,200 pounds for the trailer. Now you need to weigh the trailer, as loaded for travel. That is; full water, full propane, tools, groceries, clothes, fishing equipment, guns, ammunition, pots, pans, dishes, tableware, other kitchen utensils, etc.
Remember, if you are going to be on the road for more than a weekend, leave room in your weight calculations for souvenirs that may be added. Seashells, pretty rocks, interestingly shaped rocks, carvings, teapots, etc. They all add weight. Individually, not much, but collectively they can get real heavy!
Be careful, it is quite easy to get totally OCD about weight!

Trailerlife.com has tow ratings on their website. One thing to remember, it's not what a truck can tow (towing capacity), but what a truck can safely carry (payload capacity) that counts. You will find, particularly with half tons (150 or 1500) trucks, that they will have impressive towing capacities only to find they will never be able to get that close to towing that much as they are way overloaded on payload capacity before towing anywhere near that heavy.

The label located on your driver door jamb will indicate your payload capacity for an unloaded truck. Load up your truck with all the passengers and items you will take when towing and head to the scales, this will then indicate the remaining amount of payload left for the trailer weight (tongue or pin weight) the truck can safely carry. Tongue weight is normally between 12%-15% of a travel trailer's total weight, and pin weight a bit over 20% of a fifth wheel's total weight.

Drivers door post will give you curb and GVWR numbers. Trailer life publishes each year towing capacity for most every vehicle online.
As a simple guide,
A 1500 series truck can safely handle an average family and a TT up to around 7500 pounds Gross
A 2500 series truck can safely handle family and a TT up to about 12,000 pounds Gross or a fifth wheel up to around 12,000 Gross weight
A 3500SRW truck can handle the average family and a TT up to 14,000 pounds or so. Plus it can handle a fiver up to around 13,000 gross
A 3500 dually will go up from there.
Again, this is a guide line and not set in stone. There are just too many variables to give you more definitive information.

Glossary?
GVWR Gross Vehicle Weight Rating. This is what the mfg rates the vehicle can safely load.
GCWR Gross Combined Weight Rating. Again what the mfg certifies the vehicle and towed load can be.
Dry weight meaningless. No one will ever tow a dry trailer.