  We study the low-temperature limit of scalar perturbations of the Kerr-
AdS$_{5}$ black-hole for generic rotational parameters. We motivate the study
by considering real-time holography of small black hole backgrounds. Using the
isomonodromic technique, we show that corrections to the extremal limit can be
encoded in the monodromy parameters of the Painlev\'e V transcendent, whose
expansion is given in terms of irregular chiral conformal blocks. After
discussing the contribution of the intermediate states to the quasi-normal
modes, we perform a numerical analysis of the low-lying frequencies. We find
not only that excited perturbations are superradiant, as expected from
thermodynamical considerations, but also that the fundamental mode presents a
dynamical phase transition, becoming unstable at specific small values of the
asymptotic charges. We close by considering the holographic interpretation of
the unstable modes and the decaying process.
