  We establish the conditions for supersymmetric domain wall solutions to N=4
gauged supergravity in five dimensions. These read as BPS first-order equations
for the warp factor and the scalar fields, driven by a superpotential and
supplemented by a set of constraints that we specify in detail. Then we apply
our results to certain consistent truncations of IIB supergravity, thus
exploring their dual field theory renormalization group flows. We find a
universal flow deforming superconformal theories on D3-branes at Calabi-Yau
cones. Moreover, we obtain a superpotential for the solution corresponding to
the baryonic branch of the Klebanov-Strassler theory, as well as the
superpotential for the flow describing D3 and wrapped D5-branes on the resolved
conifold.
