  This paper studies the thermodynamic properties of the 5D black hole in
Einstein-Gauss-Bonnet gravity from the viewpoint of geometrothermodynamics. It
{is found} that the Legendre invariant metrics of the 5D black {holes} in
Einstein-Yang-Mills-Gauss-Bonnet {theory and} Einstein-Maxwell-Gauss-Bonnet
{theory} reproduce the behavior of the thermodynamic interaction and phase
transition structure of the corresponding black hole configurations
{correctly}. It is shown that they are both curved and {that} the curvature
scalar {provides} information about the phase transition point.
