  One of the simplest way to extend 4D cosmological models is to add another
spatial dimension to make them 5D. In particular, it has been shown that the
simplest of such 5D models, i.e., one in which the right hand side of the
Einstein equation is empty, induces a 4D nonempty Universe. Accordingly, the
origin of matter in the 4D real Universe might be mathematically attributed to
the existence of one (fictitious) extra spatial dimension. Here we consider the
case of an empty 5D Universe possessing a cosmological constant $\Lambda$ and
obtain exact solutions for both positive and negative values of $\Lambda$. It
is seen that such a model can naturally reduce to a power law $\Lambda$CDM
model for the real Universe. Further, it can be seen that, the arbitrary
constants and functions appearing in this model are endowed with definite
physical meanings.
