Five-dimensional supergravity in N=1/2 superspace

We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincare symmetries manifestly. The remaining four supersymmetries and the rest of the Poincare symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we discuss the construction of the 5D gravitational Chern-Simons invariant integral A perpendicular to R perpendicular to R in this superspace.