I'm also a huge Duck fan...
Anyway... as mentioned, even with the 5.3, you STILL have to abide by the truck's ratings. The 5.3 only means that it will pull the weight better than the 4.8.
For your truck (again, as mentioned) you should be most concerned with the payload capacity more than anything else. So, once you figure that out (GVWR - curb weight)you will then be able to determine how heavy (not necessarily long) of a trailer you can pull.
To weigh your truck you don't really have to load it up. Just take it to the scales (preferably with a full tank of gas) and weigh it with you in it. That will be your curb weight. Then just subtract that from your GVWR (7000 lbs) and that will be your payload. Simple.
Then weigh EVERYTHING you put on or in the truck (including passengers, pets, equipment, tools, camping stuff, etc), and subtract that from your newly acquired payload capacity and what's left over will be what you can use for the tongue weight of a trailer..and don't forget to add the weight of the weight distribution unit and sway control device.
It's really not that complicated.
Good luck
Ron