Off-shell D=5, N=2 Riemann squared supergravity

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.