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We present an off-shell formulation of matter-Yang-Mills system coupled tosupergravity in five dimensional space-time. We give an invariant action forthe general system of vector multiplets and hypermultiplets coupled tosupergravity as well as the supersymmetry transformation rules. All theauxiliary fields are kept un-eliminated so that the supersymmetrytransformation rules remain unchanged even when the action is changed.Comment: 36 pages, no figures, LaTeX, version to appear in PTP  105(2001),323-35

Off-Shell d=5 Supergravity Coupled to a Matter-Yang-Mills System