  We analyse the most general bosonic supersymmetric solutions of type IIB
supergravity whose metrics are warped products of five-dimensional anti-de
Sitter space (AdS$_5$) with a five-dimensional Riemannian manifold $M_{5}$,
where the five-form flux vanishes, while all remaining fluxes are allowed to be
non-vanishing consistent with SO(4,2) symmetry. This completes the program of
classifying all supersymmetric solutions of ten and eleven-dimensional
supergravity with an AdS$_5$ factor. We investigate the supersymmetry
conditions in some special cases, and demonstrate how these are satisfied by a
solution originally found in arXiv:1410.2650[hep-th], utilising the method of
non-Abelian T-duality.
