  We present a projective superspace formulation for matter-coupled simple
supergravity in five dimensions. Our starting point is the superspace
realization for the minimal supergravity multiplet proposed by Howe in 1981. We
introduce various off-shell supermultiplets (i.e. hypermultiplets, tensor and
vector multiplets) that describe matter fields coupled to supergravity. A
projective-invariant action principle is given, and specific dynamical systems
are constructed including supersymmetric nonlinear sigma-models. We believe
that this approach can be extended to other supergravity theories with eight
supercharges in $D\leq 6$ space-time dimensions, including the important case
of 4D N=2 supergravity.
