  We present a large class of new backgrounds that are solutions of type IIB
supergravity with a warped AdS${}_5$ factor, non-trivial axion-dilaton,
$B$-field and three-form Ramond-Ramond flux but yet have no five-form flux. We
obtain these solutions and many of their variations by judiciously applying
non-Abelian and Abelian T-dualities, as well as coordinate shifts to
AdS${}_5\times X_5$ IIB supergravity solutions with $X_5=S^5, T^{1,1},
Y^{p,q}$. We address a number of issues pertaining to charge quantization in
the context of non-Abelian T-duality. We comment on some properties of the
expected dual super conformal field theories by studying their CFT central
charge holographically. We also use the structure of the supergravity Page
charges, central charges and some probe branes to infer aspects of the dual
super conformal field theories.
