  We give an 8-dimensional realization of the Clifford algebra in the
5-dimensional Galilean space-time by using a dimensional reduction from the
$(5+1)$ Minkowski space-time to the $(4+1)$ Minkowski space-time which
encompasses the Galilean space-time. A set of solutions of the Dirac-type
equation in the 5-dimensional Galilean space-time is obtained, based on the
Pauli representation of $8\times 8$ gamma matrices. In order to find an
explicit solution, we diagonalize the Klein-Gordon divisor by using the
Galilean boost.
