  We construct new classes of exact cosmological solutions to five dimensional
Einstein-Maxwell-dilaton theory with two coupling constants for the
dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions
are non-stationary and the solutions that both coupling constants are non-zero
are almost regular everywhere. The size of spatial section of the asymptotic
metric shrinks to zero at early time and increases to infinitely large at very
late time. The cosmological constant depends on the dilaton coupling constant
and can take positive, zero or negative values.
