  The mixed spin-1/2 and spin-5/2 Ising model is investigated on the Bethe
lattice in the presence of a magnetic field $h$ via the recursion relations
method. A ground-state phase diagram is constructed which may be needful to
explore important regions of the temperature phase diagrams of a model. The
order-parameters, the corresponding response functions and internal energy are
thoroughly investigated in order to typify the nature of the phase transition
and to get the corresponding temperatures. So, in the absence of the magnetic
field, the temperature phase diagrams are displayed in the case of an equal
crystal-field on the $(k_{\textrm{B}}T/|J|, \,D/|J|)$ plane when $q=3,4$, $5$
and $6$. The model only exhibits the second-order phase transition for
appropriate values of physical parameters of a model.
