  Based on recent discussions on the so-called unconventional supersymmetry, we
propose a 5D Chern-Simons AdS-$\mathcal{N}$-SUGRA formulation without gravitino
fields and show that a residual local SUSY is preserved. We explore the
properties of CS theories to find a solution to the field equations in a 5D
manifold. With a Randall-Sundrum-type ansatz, we show that this particular
dimensional reduction is compatible with SUSY, and some classes of 4D solutions
are then analyzed.
