  Using on-shell gauge invariant formulation of relativistic dynamics we study
interaction vertices for a massive spin 5/2 Dirac field propagating in (A)dS
space of dimension greater than or equal to four. Gravitational interaction
vertex for the massive spin 5/2 field and all cubic vertices for the massive
spin 5/2 field and massless spin 2 field with two and three derivatives are
obtained. In dimension greater that four, we demonstrate that the gravitational
vertex of the massive spin 5/2 field involves, in addition to the standard
minimal gravitational vertex, contributions with two and three derivatives. We
find that for the massive spin 5/2 and massless spin 2 fields one can build two
higher-derivative vertices with two and three derivatives. Limits of massless
and partial massless spin 5/2 fields in (A)dS space and limits of massive and
massless spin 5/2 fields in flat space are discussed.
