  In the standard Einstein's theory the exterior gravitational field of any
static and axially symmetric stellar object can be described by means of a
single function from which we obtain a metric into a four-dimensional
space-time. In this work we present a generalization of those so called Weyl
solutions to a space-time-matter metric in a five-dimensional manifold within a
non-compactified Kaluza-Klein theory of gravity. The arising field equations
reduce to those of vacuum Einstein's gravity when the metric function
associated to the fifth dimension is considered to be constant. The calculation
of the geodesics allows to identify the existence or not of different
behaviours of test particles, in orbits on a constant plane, between the two
metrics. In addition, static solutions on the hypersurface orthogonal to the
added dimension but with time dependence in the five-dimensional metric are
also obtained. The consequences on the variation of the rest mass, if the fifth
dimension is identified with it, are studied.
