  Homogeneous cosmological solutions are obtained in five dimensional space
time assuming equations of state $ p = k\rho $ and $ p_{5}= \gamma\rho$ where p
is the isotropic 3 - pressure and $p_{5}$, that for the fifth dimension. Using
different values for the constants k and $\gamma$ many known solutions are
rediscovered. Further the current acceleration of the universe has led us to
investigate higher dimensional gravity theory, which is able to explain
acceleration from a theoretical view point without the need of introducing dark
energy by hand. We argue that the terms containing higher dimensional metric
coefficients produce an extra negative pressure that apparently drives an
acceleration of the 3D space, tempting us to suggest that the accelerating
universe seems to act as a window to the existence of extra spatial dimensions.
Interestingly the 5D matter field remains regular while the \emph{effective}
negative pressure is responsible for the inflation. Relaxing the assumptions of
two equations of state we also present a class of solutions which provide early
deceleration followed by a late acceleration in a unified manner. Interesting
to point out that in this case our cosmology apparently mimics the well known
quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a
smooth transition from a dust dominated model to a de Sitter like one takes
place.
