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The 5 amp field breaker in the 1976 Cessna 172M does NOT have the
alternator field current flow through it. It has only the field relay
coil current flow through it which is about 1/10 of an amp.
The alternator field current comes from the output terminal of the
alternator through the field relay and the switching transistor in the
regulator. There is NO fuse or breaker in this circuit unless you
call the 60 amp alternator breaker the field breaker.
Look it up, you will be surprised. The schematic of the regulator is
shown in the Cessna "Alternator charging Systems"Manual. The
airframe wiring is shown in the airframe service manual.
Cessna made a mistake in my opinion.

I looked it up, and you are right. My mistake. A failed field
breaker will only open the field relay, disconnecting the alternator
output from the field. I guess the 5-amp breaker is a throwback to the
generator days, when some had the regulator output run through a
breaker or fuse on the way to the field.
I agree with the 60-amp output breaker opening causing big
problems. We've duplicated that here in the shop on a demonstration
circuit. The airplane would be safer if it was wired to disconnect the
field when the output breaker pops.

Dan