As for the windings on a motor, they either work, don't work, or smoke (shorted winding) and pop a breaker. More questions:
-- Is it pumping water for the 5-10 minutes until it quiets?

Yes water is pumping fine.

-- Are there air bubbles visible in the pump basket during this period?

Minimal bubbles

-- Does it only do this on a cold start? i.e. what happens if it comes up to temperature after a half hour or so, you shut it down for 10 minutes, and restart it.

No noise after warm/shutdown/restart

-- What is the filter pressure doing during this 5-10 minute period of noise?
Gauge not working now

-- Does the noise gradually disappear or is it suddenly quiet?

I think it just fads away. Usually happens at morning startup go inside, come back, no noise.

-- Did this problem suddenly appear or did it come on gradually?

Did it last year also, pump is 5 years old, just wondering if I should or can do anything.

gg