The way I figure it, you need a minimum of three people to keep a working spaceship in service. By “working spaceship” I mean some sort of commercial space transport, common to the era, ferrying goods and passengers among various ports of call.

First, you need the business manager. It’s his job to decide where to go, what to buy and sell, who to deal with, and generally handle the economic functions of the ship. He does the payroll, hiring and firing, paying for stuff like fuel, food, spare parts, and whatnot. Since running the ship is first and foremost a business, this is the guy in charge, the captain, and probably the owner. He does the top-level decision making for the purpose of maximizing the profit of each trip.

Second, you need someone to fly the ship. This includes maneuvering, navigation, reading and interpreting sensor data, taking off and landing, and communicating with the ground or other ships. You could have multiple people, each doing one of these tasks, but you need one guy at least.

Third, you need someone to keep the ship running. Call them an engineer or a mechanic or the maintenance guy. His job is to keep the ship’s mechanical systems operating properly, repairing things when they break, and jury-rigging patches to keep the crew alive until the opportunity arises to make more lasting repairs.

Potentially, one person could do all of that. Or one person and a Wookiee. Odds are, most of the time, the business manager won’t have all that much to do while the ship is in transit, and to the extent that he would it would involve telling the others what to do. He could just as easily skip that step and do it himself. However, there would inevitably be times when the reactor threatens to go supercritical at the same time the ship desperately needs to avoid crashing into space debris.

So, division of labor is a good idea.

There are other things that need to be done on board ship, of course. Someone has to cook. Someone has to clean the toilets. A stevedore would be nice to carry around heavy stuff. Someone with medical training would be an asset. Someone needs to deal with the passengers. But that stuff could be folded into the skillsets of the existing three crewmen. The business manager/captain could double as the second pilot/mechanic.

That brings up the matter of shifts. As dedicated as the pilot or mechanic may be, they can’t be on the job 24/7. Sometimes, things will need attention when they are unable to attend to it. This suggests the need for two more people who can cover the off-shifts. On the other hand, most of space travel is ballistic ballet, which generally takes care of itself. So maybe the base three could work as needed rather than having shifts at all.

So, yeah. Three people. Maybe five. Unless I’ve forgotten something that someone needs to tell me about in the comments.