  We show that the Bekenstein-Hawking entropy of a class of BPS electrically
charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple
extremization principle. We expect that this extremization corresponds to the
attractor mechanism for BPS rotating black holes in five-dimensional gauged
supergravity, which is still unknown. The expression to be extremized has a
suggestive resemblance to anomaly polynomials and the supersymmetric Casimir
energy recently studied for $\mathcal{N}=4$ super Yang-Mills.
