Bill,

A reliable way to find the effective shunt capacitance is to observe
the self-resonant frequency of the coil. If it's really about 25pF,
and the coil really is about 5mH, I'd expect self-resonance at about
450kHz. Can you make some simple measurement of the self resonance?
(e.g., square wave coupled loosely to the coil; scope monitoring the
ringing. Or signal generator swept across the suspected frequency
range, looking for a peak in the response. Key is to couple the
generator and the detector to the coil loosely.)

Cheers,
Tom