Lets pick the Akira (the ship of which I am a commander on). Note here, I went with the Engineering option when I started the game. According to the ship specifications, I get one engineer slot, one science slot, and three tactical slots. Main characters I'm assuming aren't taken in to account here? ~ I only state that because I have one engineer slot on the Akira, and that's being taken up by a bridge officer. I'm not sure whether main characters are actually included where slots are concerned.
My current characters are an Engineer (main character), another Engineer (lieutenant commander), one Science (lieutenant), and two Tactical (one ensign, the other lieutenant commander). Now apparently, I should be able to have a third Tactical Officer, but I don't. I have a few candidates, but I can't use them because there 'isn't enough room for them to join my crew'.
I have a total of five character slots (this is including my main character) yet when you get to vice admiral and such, it shows you to have at least nine bridge officers. Obviously I'm not entitled to nine bridge officers yet, and am only allowed five (though I can only have four). That being said, I'm pretty sure I could still have five slots when I was flying around in my Centaur-type.