  Recent one-loop calculations of certain supergravity-mediated quantum
corrections in supersymmetric brane-world models employ either the component
formulation (hep-th/0305184) or the superfield formalism with only half of the
bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216).
There are reasons to expect, however, that 5D supergraphs provide a more
efficient setup to deal with these and more involved (in particular,
higher-loop) calculations. As a first step toward elaborating such supergraph
techniques, we develop in this letter a manifestly supersymmetric formulation
for 5D globally supersymmetric theories with eight supercharges. Simple rules
are given to reduce 5D superspace actions to a hybrid form which keeps manifest
only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were
carefully worked out by rewriting the component actions in terms of simple
superfields). To demonstrate the power of this formalism for model building
applications, two families of off-shell supersymmetric nonlinear sigma-models
in five dimensions are presented (including those with cotangent bundles of
Kahler manifolds as target spaces). We elaborate, trying to make our
presentation maximally clear and self-contained, on the techniques of 5D
harmonic and projective superspaces used at some stages in this letter.
