In the framework of restricted five-body problem, the existence and stability of the libration points are explored and analysed numerically, under the effect of non–isotropic mass variation of the fifth body (test particle or infinitesimal body). The evolution of the positions of these points are illustrated, as a function of the perturbation parameter. We perform a systematic investigation in an attempt to understand how the perturbation parameter due to variable mass of the fifth body affects the positions, movement and stability of the libration points. In addition, we have revealed how the basins domain of convergence associated with the libration points are substantially influenced by the perturbation parameter.