We show that the empty five-dimensional solutions of
Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in
the "old" Kaluza-Klein gravity, under appropriate interpretation can generate
an ample variety of cosmological models in 4D, which include the
higher-dimensional modifications to general relativity predicted by "modern"
versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld
theories. This is the first time that these solutions are investigated in a
systematic way as embeddings for cosmological models in 4D. They provide a
different formulation, which is complementary to the approaches used in current
versions of 5D relativity.Comment: Accepted for publication in JHE
