  We study a five-dimensional non-relativistic gravity theory whose action is
composed of a gravitational sector and a sector of matter where the
gravitational sector is given by the so called Newton--Chern--Simons gravity
and where the matter sector is described by a perfect fluid. At time to do
cosmology, the obtained field equations shows a close analogy with the
projectable version of the Ho\v{r}ava--Lifshitz theory in (3+1)-dimensions.
Solutions and their asymptotic limits are found. In particular a phantom
solution with a future singularity reminiscent of a Litlle Big Rip future
singularity is obtained.
