  We investigate vacuum static black hole solutions of Einstein-Gauss-Bonnet
gravity with a negative cosmological constant in five dimensions. These are
solutions with horizons of nontrivial topologies. The first one possesses a
horizon with the topology $S^1 \times H^2$, and a varying Gauss-Bonnet coupling
constant $\alpha$. By looking into its thermodynamic properties, we find that
its specific heat capacity with fixed volume is negative, therefore it is
thermodynamically unstable. The second one is equipped with a so-called
"Sol-manifold" as its horizon, and interestingly, the product of the
Gauss-Bonnet coupling constant $\alpha$ and the cosmological constant $\Lambda$
is fixed. For the second solution, the total energy and entropy vanish. These
results enlarge our knowledge of both topological black holes in higher
dimensions and the property of higher curvature corrections of gravitational
theories.
