I have a 2006 Burb now and they are not kidding that its not going to win a races against turtles up any hills, but with the WD and E-Brake setup I don't feel its to much for the burb. Plus I keep our speeds low and take my time. I did install a second after market tranny cooler to help also.
I had a tough time finding a trailer that would fit my family and still be "within" weight. I'm def. pushing our limits right to the edge(maybe a little past the edge), but like I said take my time and give the TV a number of breaks. Most of my trips are local withing 15 miles. Once every couple of years we go up north to the mountains and that's the drive I feel it the most.
I like that 5K lb range, but does depend on how much gear you need to haul. I never tow with water. I pick it up close to final camping ground which does add to the travel plan headache but saves me on the weight.
Maybe an nice ultra light that can fit your family will be the way to go. Its amazing how light they can make them now. My TT is an 07 its a beast in weight.
GL in your search!