  We reformulate maximal D=5 supergravity in the consistent approach uniquely
based on Free Differential Algebras and the solution of their Bianchi
identities (= rheonomic method). In this approach the lagrangian is unnecessary
since the field equations follow from closure of the supersymmetry algebra.
This enables us to explicitly construct the non-compact gaugings corresponding
to the non--semisimple algebras CSO(p,q,r), irrespectively from the existence
of a lagrangian. The use of Free Differential Algebras is essential to clarify,
within a cohomological set up, the dualization mechanism between one-forms and
two-forms. Our theories contain 12-r self-dual two-forms and 15+r gauge
vectors, r of which are abelian and neutral. These theories, whose existence is
proved and their supersymmetry algebra constructed hereby, have potentially
interesting properties in relation with domain wall solutions and the trapping
of gravity.
