  In this paper we present a complete classification of the isolated central
configurations of the five-body problem with equal masses. This is accomplished
by using the polyhedral homotopy method to approximate all the isolated
solutions of the Albouy-Chenciner equations. The existence of exact solutions,
in a neighborhood of the approximated ones, is then verified using the Krawczyk
method. Although the Albouy-Chenciner equations for the five-body problem are
huge, it is possible to solve them in a reasonable amount of time.
