Exact cosmological solutions are obtained in a 5D Kaluza--Klein type of spacetime for an inhomogeneous distribution of fluid obeying an equation of state , where k is a constant, p is the isotropic pressure in the three space and is that corresponding to the extra fifth dimension. The set of solutions includes those of dust, radiation and stiff fluid confined to the usual three-dimensional space, while the pressure monotonically decreases with time. In another solution for k=-1, the spacetime exhibits isotropic, exponential expansion in the 3-space conforming to the inflationary scenario. Depending on the signature of the 4-space curvature it can be shown that as the 3-space expands, the extra space is amenable to dimensional reduction with time. This is quite desirable in the context of multi-dimensional cosmology. Further the entropy generation in the physical 3-space resulting from the compactification of the fifth dimension is discussed. Encouraging to note is that apart from the well known singularity at the big bang our inhomogeneous solutions are otherwise regular. Further, our model seems to suggest an alternative mechanism pointing to a smooth pass over from a primordial multidimensional, inhomogeneous phase to a four-dimensional homogeneous one.