  We present novel classes of non-stationary solutions to the five-dimensional
generalized Einstein-Maxwell-dilaton theory with cosmological constant, in
which the Maxwell's filed and the cosmological constant couple to the dilaton
field. In the first class of solutions, the two non-zero coupling constants are
different while in the second class of solutions, the two coupling constants
are equal to each other. We find consistent cosmological solutions with
positive, negative or zero cosmological constant, where the cosmological
constant depends on the value of one coupling constant in the theory. Moreover,
we discuss the physical properties of the five-dimensional solutions and the
uniqueness of the solutions in five dimensions by showing the solutions with
different coupling constants, can't be uplifted to any Einstein-Maxwell theory
in higher dimensions.
