Yes, if you put *all* the weight on one beam. You have two beams so the load will be 1/2 of that, giving you a deflection (calculated) of 19 inches. That's still probably way too much, and I don't know if the beam is being stressed beyond safe limits. Now in reality with your long wheel-base you don't have a single-point load, so the deflection won't be as extreme.If I'm doing that correctly, it says putting 2500 lbs in the middle will result in almost 3 feet of deflection. That's a little more than I had in mind.
Steam's strut / stay suggestion may be a reasonable approach, but I'm not a mechanical engineer and wouldn't know how to accurately calculate the forces.