  The recent construction of the non-semisimple gaugings of maximal D=5
supergravity is reported here. This construction is worked out in the so-called
rheonomic approach, based on Free Differential Algebras and the solution of
their Bianchi identities. In this approach the dualization mechanism between
one-forms and two-forms is more transparent. The lagrangian is unnecessary
since the field equations follow from closure of the supersymmetry algebra.
These theories contain 12-r self-dual two-forms and 15+r gauge vectors, r of
which are abelian and neutral. Such theories, whose existence has been proved
and their supersymmetry algebra constructed, have potentially interesting
properties in relation with domain wall solutions and the trapping of gravity.
