  We consider the bosonic and fermionic symmetries of five-dimensional Maxwell-
and Yang-Mills-Einstein supergravity theories on a spacetime with boundaries
(isomorphic to M x S1/Z2). Due to the appearance of the "Chern-Simons" term,
the classical action is not generally invariant under gauge and
supersymmetries. Once bulk vector fields are allowed to propagate on the
boundaries, there is an "inflow" governed by the rank-3 symmetric tensor that
defines the five-dimensional theories. We discuss the requirements that
invariance of the action imposes on new matter content and boundary conditions.
