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.