Five-Dimensional Gauged Supergravity and Supersymmetry Breaking in $M$~Theory

We extend the formulation of gauged supergravity in five dimensions, as obtained by compactification of $M$~theory on a deformed Calabi-Yau manifold, to include non-universal matter hypermultiplets. Even in the presence of this gauging, only the graviton supermultiplets and matter hypermultiplets can couple to supersymmetry breaking sources on the walls, though these mix with vector supermultiplets in the bulk. Whatever the source of supersymmetry breaking on the hidden wall, that on the observable wall is in general a combination of dilaton- and moduli-dominated scenarios.