  Rapidly rotating Myers-Perry-AdS$_5$ (MPAdS$_5$) black holes are shown to be
unstable against rotational superradiance of a Maxwell field. From the onset of
the instability, time-periodic neutral black hole solutions equipped with a
nontrivial electromagnetic wave are obtained, which we call {\it photonic black
resonators}. In the horizonless limit, they reduce to geon solutions which may
be called {\it photon stars}. Specifically, we introduce a cohomogeneity-1
ansatz for the metric and Maxwell field and construct such solutions with an
$R\times SU(2)$ isometry group. We compute thermodynamic quantities and obtain
phase diagrams. It turns out that a photonic black resonator has a higher
entropy than a MPAdS$_5$ black hole, while it also has a smaller entropy than a
black resonator without the Maxwell field. This suggests what is expected for
nonlinear dynamics following the Maxwell superradiant instability with the
$SU(2)$ isometry.
