  We present a new family of asymptotically locally AdS$_5$ squashed
supersymmetric black hole solutions of Fayet-Iliopoulos gauged ${\cal N}=2$,
$D=5$ supergravity with two vector multiplets that have a natural uplift to
type IIB supergravity. Our new family of black holes is characterized by three
parameters, of which two control the horizon geometry while the latter
regulates the squashing at the boundary. We evaluate the main physical
properties of the family of solutions using holographic renormalization and
find that the entropy is independent on the squashing and it is reproduced by
using the angular momentum and the Page charges. In previously known solutions
Page and holographic charges are equal, due to the vanishing of the
Chern-Simons term that here, instead, is relevant. This result suggests that
for asymptotically locally AdS$_5$ solutions we should refer to the Page
charges to describe the thermodynamics of the system.
