Only four of those people actually make up the Elite 4.
The other person is the Champion, who is pretty much the most powerful person in the region. They were able to not only beat the Elite 4, but also beat the previous champion (except in the case of Alder, who was asked to be Champion.)
However, the Champion, while not being part of the Elite 4, is considered to lead the Elite 4. So I can understand the confusion.