New 5th Wheel & New Truck - Running nose high - UGH!!

4"-5" nose high is a very small angle over the length of the trailer. If you have the typical leaf spring suspension, the weight shift (unloading the pin) is likely not measureable. The spring equalizers should do their job (if there is no binding) and there should not be much load difference between the axles.

However, I suggest you contact the frame and suspension manufacturer (engineering not sales). Hearing straight from them should give you ground truth.