One of the most distinguished way to probe cosmological equations presenting the dynamics of homogeneous and isotropic universe which are actually ordinary differential equations is to deal them in the form of dynamical systems. These systems develop a quantitative understanding of cosmological dynamics by using analytical techniques for the underlying models. In this paper, we investigate the cosmological solutions of various models in the realm of five-dimensional Einstein Chern–Simons cosmology. We consider various interaction terms both linear and non-linear to analyze the dynamical stability of the models in the context of five-dimensional Einstein Chern–Simons gravity for the late-time accelerated universe. Finally, we examine the critical points with their corresponding trajectories for underlying models in the phase space of evolved dynamical parameters and compare our findings with the current observational data that turn out to be consistent and compatible.