**Abstract:**

Following the idea of the induced matter theory, for a non-vacuum five-dimensional version of general relativity, we propose a model in which the induced terms emerging from the extra dimension in our four--dimensional space--time, supposed to be as dark energy. Then we investigate the FLRW type cosmological equations and illustrate that when the scale factor of the fifth dimension has no dynamics, in early time the universe expands with deceleration and then in late time, expands with acceleration. In this case, the state parameter of the effective dark energy has a range of $-1<\bar{w}_{_{X}}<0$ and it has the value $-1/2$ for present time. The results for current acceleration impose that $\Omega_{_{X\circ}}>2\Omega_{_{M\circ}}$ which is in agreement with the measurements. We show that the effective energy density of dark energy have been having the same order of magnitude of the effective energy density of matter from the early time in the decelerating epoch of the universe expansion until now. The model avoids the cosmological coincidence problem.