Terms:
Continuity means electron flow is possible.
5 ohms is still continuity. Your field coil should read 5 ohms between its coil wires and only one of those wires should read zero ohms to engine/ frame (green).
If you supply 12v to a field coil, it has no choice but to make a magnetic field. Law of physics.
If the energized field core metal spins (the rotor), the magnetic field with alternate pos to neg, etc.
This alternating field excites the stator windings and produces an AC votltage in those windings. Then the rectifier converts that AC voltage to DC voltage which can be used by the bike's systems and battery.
I don't know the conditions under which your vreg "fried". But, a measured 5 ohm field coil should not be a cause for a properly designed and functional regulator. However, if the battery was ever connected in reverse polarity, even momentarily, that would be sufficient to cause any number of failures in a combo reg/ rectifier unit, and the interconnected wires as the battery dumps all its power into those items. The system is not fused, unless you consider the weakest component in the operating circuit to open as a "fuseable link".
Cheers,