I'm not far enough in my game to test with a new shipyard, but with my starting one here is how it goes:
As I expand, I do not colonize the planet immediatly next to my home world (same solar system).
As I colonize new worlds, I add them as sponsors to my shipyard until there 5/5.
Then I colonize that small planet right next to my homeworld and it is automatically added as a sponsor of my starting shipyard, so I get 6/5 sponsors.