  Junction conditions for vacuum solutions in five-dimensional
Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two
spherically symmetric regions of space-time are joined in such a way that the
induced stress tensor on the junction surface vanishes. So a spherical vacuum
shell, containing no matter, arises as a boundary between two regions of the
space-time. A general analysis is given of solutions that can be constructed by
this method of geometric surgery. Such solutions are a generalized kind of
spherically symmetric empty space solutions, described by metric functions of
the class $C^0$. New global structures arise with surprising features. In
particular, we show that vacuum spherically symmetric wormholes do exist in
this theory. These can be regarded as gravitational solitons, which connect two
asymptotically (Anti) de-Sitter spaces with different masses and/or different
effective cosmological constants. We prove the existence of both static and
dynamical solutions and discuss their (in)stability under perturbations that
preserve the symmetry. This leads us to discuss a new type of instability that
arises in five-dimensional Lovelock theory of gravity for certain values of the
coupling of the Gauss-Bonnet term. The issues of existence and uniqueness of
solutions and determinism in the dynamical evolution are also discussed.
