  In this paper we find the most general self-similar, homogeneous and
isotropic, Ricci flat cosmologies in 5D. These cosmologies show a number of
interesting features: (i) the field equations allow a complete integration in
terms of one arbitrary function of the similarity variable, and a free
parameter; (ii) the three-dimensional spatial surfaces are flat; (iii) the
extra dimension is spacelike; (iv) the general solution is Riemann-flat in 5D
but curved in 4D, which means that an observer confined to 4D spacetime can
relate this curvature to the presence of matter, as determined by the Einstein
equations in 4D. We show that these cosmologies can be interpreted, or used, as
5D Riemann-flat embeddings for spatially-flat FRW cosmologies in 4D. In this
interpretation our universe arises as a topological separation from an empty 5D
Minkowski space, as envisioned by Zeldovich.
