How much ductwork is attached to the air handler on supply side and return side? A picture would be useful.
A 5 ton air handler will typically do 2000 cfm @ 1/2" external static. Without adequate static, the same unit can do 2500 cfm or more, and in the process it keeps the coil temperature too high to achieve dehumidification. At the same time, since not much capacity is going toward removing the latent load, it will pull the space temp down fast as all capacity is directed to sensible load.
A simple check would be to measure the temperature drop across the ahu. Using a known good thermometer, check the inlet and outlet temperatures at the unit. The drop should be in the 20°F range. If less, the unit could be handling too much air (or the system could be undercharged). If the system has minimal ductwork, as is often the case with systems in open areas like this, my bet would be on too much air.
If the fan motor is a standard multi-speed PSC, changing the motor speed is as simple as moving the cooling speed connector at the molex connector near the fan motor. If the motor is the ECM type, you'd need the installation instructions to see how to change speed.
Also, any time I ever installed a system in this type building, it was necessary to let the ahu fan run continuously as opposed to cycling it with the condensing unit to maintain the best comfort conditions in the space.
If this is a relatively new installation, typically within the last year, all the above would normally be the responsibility of the installer to provide a properly functioning system under the warranty.