<p>In this paper, we investigate a (4 + 1)-dimensional nonlinear evolution equation using Lie symmetry analysis, resulting in nine infinitesimal generators. The motivation behind this study is to find analytical solutions to the governing equation, which has a wide range of applications in physical and mathematical contexts, especially fluids and plasmas, due to its ability to model complex wave phenomena in multiple spatial dimensions. We have developed both the commutator table and the adjoint table for the obtained generators. We then use a systematic and rigorous approach to develop the optimal system, utilizing the invariant properties of the adjoint transformation. This optimal system yields similarity reductions, transforming the governing partial differential equation into another equation with fewer independent variables. These transformed partial differential equations yield invariant solutions to the governing equation. The three-dimensional graphical representations demonstrate the dynamic characteristics of some of the identified solutions. These graphs may be utilized by the scientists, engineers and mathematicians to efficiently monitor various complicated physical events like fluid flow behavior, predicting natural phenomena and ion-acoustic waves. Finally, we study self-adjointness and deduce conservation laws for each infinitesimal generator.</p>