Your first way of figuring is the right way, and a 5k lb trailer would be about your maximum, if you truly have a payload of 1,635 lbs.
In 2006 there should be a yellow and white tire loading sticker on your driver's door panel. This should read the total payload of people and gear, and of course WDH/tongue weight would be included, not to exceed XXXX. If this is 1635 you are good to go with the 5K max trailer.
It is nice to have a buffer, and not tow at the very limit, but not really necessary IMO. Many tow way over limits, don't know any better/don't care!
You are wise to do the research, and ask questions!!
Jerry