When people talk about a "Big Four" or a "Big Five", they are talking about professional team sports. So, they aren't including college football or basketball or Nascar, or professional golf or tennis or boxing or anything like that.
I very strongly believe there is a Big Five, and not a Big Four. It really pisses me off when articles use the former, as in "Michael Sam is the first openly gay player in a Big Four professional league", which completely ignores Robbie Rogers.
I don't think there is any question there is a Big Five. No, we aren't in the same neighborhood as pro football, but don't try to tell me we aren't in the same neighborhood as hockey! I would say we are ahead, but I understand if people differ on that. Much of it depends upon the metrics one uses, but we are ahead in attendance per game, for example.