A 5000 pound tow rating is adequate, though not generous, so you should be OK there. Of course the advertised tow rating for every vehicle, including the Pilot, comes with the words "when properly equipped". It is up to you to determine whether your specific vehicle (not just that particular model) is "properly equipped". If you follow the spec sheet far enough, it will tell you what it means.
The Pilot has kind of a short wheelbase, which increases the need for a WDH, so you should plan on using one. Why? The hitch weight of the trailer presses down on the rear end of any tow vehicle, which raises (unweights) the front end teeter-totter style. Since the front end of the vehicle does most of the braking and all of the steering, removing weight reduces its grip on the road, which is dangerous. Unweighting is worse on short-wheelbase vehicles. A WDH moves some of that weight back to the front end, where it is needed. That is its primary function - hence the name "weight distribution".
A note on WDH's. When the front end is unweighted, it rises, and the headlights point upward. Some folks cure the headlight issue by jacking up the rear end of the tow vehicle with air bags, but that doesn't replace the weight that is missing on front end. It only gives you a false sense of safety. I recommend against it. Do it right - get a WDH.
