  We show that the Lagrangian of the free spin-5/2 field in the spinor-tensor
representation with the auxiliary spinor field depends on the three arbitrary
parameters. The first two parameters are associated with the spin-3/2 and -1/2
sector of the theory while the latter one is related to the auxiliary degrees
of freedom. We derive a corresponding propagator of the system which represents
(2 x 2) matrix in the $(\psi_{\mu\nu},\xi)$ space. The diagonal terms stand for
the propagation of the spin-5/2 and auxiliary fields whereas the non-diagonal
ones correspond to the $\psi_{\mu\nu}-\xi$ mixing. The resulting spin-5/2
propagator contains non-pole contributions coming from the spin-3/2 and -1/2
sector of the spinor-tensor representation. A general form of the interaction
vertex involving spin-5/2 field is discussed on the example of the $\pi N
N^*_{5/2}$ coupling. It is demonstrated that lower spin degrees of freedom can
be removed from the theory by using higher order derivative coupling.
