Abstract In this research, we explore the cosmological implication on five-dimensional FRW cosmological models for $k=-1,0,1$ in presence of two perfect fluids: ordinary baryonic fluid and a bizarre creating dark energy in the context of Lyra's manifold. We obtain the exact solution of the equation by assuming the parametrization of the Hubble parameter $H(a) = \tau(1+a^{-\nu})$, where $a$ is a scale factor and $ \tau>0$, $\nu>1$ are the arbitrary constants and the relation between metric coefficients $B = A^{n}$, where $ n \neq 0 $ is a constant. The result in the transition from a previously decelerating universe to the current accelerating universe, characterized by a time-dependent deceleration parameter. Moreover, we have used 46 observational Hubble data sets to restrict the parameters of our suggested model. Some cosmological parameters have been examined about the nature of the proposed model universe. As such, our model can be considered a realistic one.