  We construct a Schwarzschild-type exact external solution for a theory of
gravity admitting local Galilean invariance. In order to realize the Galilean
invariance we need to adopt a five-dimensional manifold. The solution for the
gravitational field equations obeys a Birkhoff-like theorem. Three classic
tests of general relativity are analyzed in detail: the perihelion shift of the
planet Mercury, the deflection of light by the Sun, and the gravitational
redshift of atomic spectral lines. The Galilean version of these tests exhibits
an additional parameter $b$ related to the fifth-coordinate. This constant $b$
can be estimated by a comparison with observational data. We observe that the
Galilean theory is able to reproduce the results traditionally predicted by
general relativity in the limit of negligible $b$. This shows that the tests
are not specifically Lorentz invariant.
