The structure of the families was constantly in flux due to the actions of one of the mafia's bosses, Capone Bege, who frequently took down his rival bosses in order to watch the struggle for power that would ensue. The other mafias tried to attack Bege in revenge, but all of their attack parties were dispatched due to Bege's Devil Fruit power.
However, Bege's presence in the West Blue ceased after he grew tired of his dominance and set sail on the Grand Line as a pirate. It is unknown if the other four families are currently active.
They are possibly based off the real-life Five Families, which were the five major crime families controlling New York.