I'm going to stick my head out on a limb here.

The oldest true profession is medicine man/medicine woman. That is to say the person who was the clan's healer and priest.

Hunting is not a profession when half the clan does it. Farmer was not considered a profession in the Middle Ages, it was considered the default of people who didn't have a profession. There is no profession surname that represents farmers (The surname Farmer comes from the Old French fermier...which meant tax collector).

So #5 is the true oldest profession, because it was something somebody did, full time, that was not the same as what everyone else did.

IMO.