I think you need to know if 5 gpm is going to drain the sump in a short period of time.
That's a lot of water. 300 gallons in an hour? (6) 50 gal barrels..
In 10 hours, that's going to be 3,000 gallons.
Anyways, I think the Chilled-Water AC we have at work, pre-cools the water down
to about 45 degrees. It's sent into big water-to-air exchangers in the ceilings and cold air comes down out of the ducts..
It works too well.. I have to wear a jacket sometimes.. In July & August!!
If you have an endless supply of cool water, I would not spend much
money on hardware to prove the idea will work.
Just build the actual unit..