Five-dimensional gravitational super Chern-Simons terms

We consider the Chern-Simons five-form C5(CS) for the five-dimensional antide Sitter superalgebra SU(2,21), whose exterior derivative is equal to dABCRCRBRA where RA are the full group curvatures and dABC are the invariant d symbols of SU(2,21). Under the simple local five-dimensional supersymmetry transformations, C5(CS) is not invariant. Its relation to the invariant action of simple five-dimensional supergravity in the group-manifold formulation is given.