  We numerically explore the structure of quasi-normal (QN) frequencies of the
five-dimensional small and large Kerr-anti de Sitter (Kerr-AdS${}_5$) black
hole with equal and unequal rotations. Our investigation also covers low and
high Hawking temperatures. We then study the stability of the Kerr-AdS${}_5$
black hole and the structure of highly damped QN modes, which would reflect the
thermodynamic property of the Kerr-AdS${}_5$ black hole. We find that the
highly damped complex QN frequencies of a nearly maximally spinning
Kerr-AdS${}_5$ black hole have the periodic separation of the surface gravity
at the horizon in the imaginary part while the real part converges to the
superradiant frequency, which may be relevant to the pole structure of the
thermal Green's function in the corresponding conformal field theory on the
Kerr-AdS${}_5$ boundary. Finally, we discuss a relation between the QN modes of
the Kerr-AdS${}_5$ black hole and the Hod's conjecture on the horizon area
quantization along with the analysis of the horizon topology of the
Kerr-AdS${}_5$ black hole. We show that in general, an ultra-spinning
Kerr-AdS${}_5$ black hole, whose spin parameter is infinitesimally close to the
AdS curvature radius, has its non-compact horizon, and based on the Hod's
conjecture, we argue that the horizon area may be continuous, that is, the unit
area of the horizon vanishes in the ultra-spinning regime.
