  We extend the direct quantum approach of the standard FRW cosmology from 4D
to 5D and obtain a Hamiltonian formulation for a wave-like 5D FRW cosmology.
Using a late-time approximation we isolate out a y-part from the full wave
function of the 5D Universe. Then we find that the compactness of the fifth
dimension y yields a quantized spectrum for the momentum $P_{5}$ along the
fifth dimension, and we show that the whole space-part of the wave function of
the 5D Universe satisfies a two-dimensional Schr\"odinger equation.
