  We develop an invariant approach to $SU(2)$--structures on spin
$5$--manifolds. We characterize (via spinor approach) the subspaces in the
spinor bundle which induce the same group isomorphic to $SU(2)$. Moreover, we
show how to induce quaternionic structure on the contact distribution of
considered $SU(2)$--structure. We conclude with the invariance of certain
components of the covariant derivative $\nabla\varphi$, where $\varphi$ is any
spinor field defining considered $SU(2)$--structure. This shows, what expected,
that (at least some of) the intrinsic torsion modules, can be derived
invariantly with the spinorial approach.
