  In the framework of restricted five bodies 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 and the
possible regions of motion 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 domain of the basins of convergence associated with the
libration points are substantially influenced by the perturbation parameter.
