  In this paper, using $f(R)$ theory of gravity we explicitly calculate
cosmological evolution in the presence of a perfect fluid source in four and
five dimensional, space time in which this cosmological evolution in
self-creation is presented by Reddy et al 2009 Int. J. Theor. Phys. 48 10. An
exact cosmological model is presented using a relation between Einstein gravity
field equation components due to a metric with the same component from $f(R)$
theory of gravity. Some physics and kinematical properties of the model are
also discussed.
