  In this paper, we consider a class of five-dimensional Ricci-flat vacuum
solutions, which contain two arbitrary functions $\mu(t)$ and $\nu(t)$. It is
shown that $\mu(t)$ can be rewritten as a new arbitrary function $f(z)$ in
terms of redshift $z$ and the $f(z)$ can be determined by choosing particular
deceleration parameters $q(z)$ which gives early deceleration and late time
acceleration. In this way, the $5D$ cosmological model can be reconstructed and
the evolution of the universe can be determined.
