  We construct a new off-shell invariant in N=2, D=5 supergravity whose leading
term is the square of the Riemann tensor. It contains a gravitational
Chern-Simons term involving the vector field that belongs to the supergravity
multiplet. The action is obtained by mapping the transformation rules of a spin
connection with bosonic torsion and a set of curvatures to the fields of the
Yang-Mills multiplet with gauge group SO(4,1). We also employ the circle
reduction of an action that describes locally supersymmetric Yang-Mills theory
in six dimensions.
