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 Poincar'e symmetries manifestly. The remaining four supersymmetries and the rest of the Poincar'e 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 construct the $\int A\wedge R\wedge R$ invariant in this superspace.