  We uncover the solution space of a five dimensional geometry which we deem it
as the direct counterpart of the Bianchi Type V cosmological model. We
kinematically reduce the scale factor matrix and then, with an appropriate
scaling and choice of time, we cast the spatial equations into a simple
``Kasner'' like form; thus revealing linear integrals of motion. Their number
is enough so that, along with the quadratic constraint, it suffices to scan the
entire space of solutions. The latter is revealed to be quite rich, containing
cosmological solutions, some of which admit dimensional reduction
asymptotically to four dimensions, Kundt spacetimes with vanishing type I
(polynomial) curvature scalars and solutions describing periodic universes
which behave like cosmological time crystals.
