Colleagues, please tell me how the economy (production) works in the game.
Production 5 is high enough to supply an arbitrary number of Demand 5 industries. This includes Export, so yes, you're getting paid for your full production even if you're using some of it.
You'll even get paid for exports if you've got a Demand 6 somewhere that requires you to import as a supplement, too - note that having to import goods just increases your upkeep costs and doesn't require spending money beyond that.
Note also that your imports and exports are capped by your accessibility - with only 40% access, you won't be able to export more than 4 Production worth of goods to the other factions' planets in the Core, or import enough to meet more than 4 Demand with their goods.