My TV is a 2003 Mitsubishi Montero Sport rated to pull 5000 lbs. I've had a few people comment, when I hook up, that the TV drops too much in the back. One guy commented that the shocks may have weakened over the years. The tongue weight of my Hi-Lo is within limits for the TV according to the book.
I'm thinking of having new shocks put on. Are there shocks recommended for tow vehicles...heavy duty types? Anyone have comments or a recommendation?

Having good shocks is important, however, the shocks have nothing to do with how much your tow vehicle drops with the trailer attached, that is a function of the springs. It sounds like you need a weight distributing hitch, or if you already have one it needs adjusted. Having good shocks will improve the ride by reducing bouncing up and down, and saves wear and tear on other suspension components.

Added thought, you may want to check your springs for broken leaves or coils. I had that happen on my '02 Explorer from towing a popup trailer without WDH. They take quite a pounding especially when there is added weight being hauled.