  Using numerical algebra tools, new classes of monopole solutions are obtained
to the static, spherically-symmetric vacuum field equations of five-dimensional
general relativity. First proposed by Kaluza, 5D general relativity unites
gravity and classical electromagnetism with a scalar field. These monopoles
correspond to bodies carrying mass, electric charge, and scalar charge. The
Reissner-Nordstr\"om limit allows us to constrain the signature of the fifth
component to be spacelike, but valid solutions are obtained for either sign of
the scalar field. We find that Kaluza vacuum solutions imply the scalar field
energy density is the negative of the electric field energy density, so the
total electric and scalar field energy of the monopole is zero. Yet the new
solutions provide reasonable Reissner-Nordstr\"om and Coulomb limits in
mathematical form, with varying possibilities for the scalar field. The
vanishing of the total electric and scalar field energy density for vacuum
solutions seems to imply the scalar field can be understood as a
negative-energy foundation on which the electric field is built.
