That sounds like a loose fitting that will hold back the water in the tank (low head pressure) but starts to suck air in when the pump runs and the head pressure from the tank has decreased a bit.
Also look for a kink or compression of the line from the tank to the inlet of the pump. I am not familiar with your 5th'er but tracing the line could uncover something. Also look for a winterizing valve on the pump inlet side, sometimes these will cause the same if they leak or are not 100% off.
Good luck.
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