  We consider the Einstein-Gauss-Bonnet equations in five dimensions including
a negative cosmological constant and a Maxwell field. Using an appropriate
Ansatz for the metric and for the electromagnetic fields, we construct
numerically black holes with two equal angular momenta in the two orthogonal
space-like planes of space-time. Families of such solutions, labeled by the
angular momentum and by the electric charge are obtained for many
representative intervals of the Gauss-Bonnet coupling constant $\alpha$. It is
argued that, for fixed values of $\alpha$, the solutions terminate into
extremal black holes at ($\alpha$-dependent) critical values of the angular
momentum and/or of the electric charge. The influence of the Gauss-Bonnet
coupling constant, of the charge and of the cosmological constant on the
thermodynamics of the black holes and on their domain of existence is analyzed.
