  We study AdS$_5$ black holes from a recently suggested giant graviton
expansion formula for the index of $U(N)$ maximal super-Yang-Mills theory. We
compute the large $N$ entropy at fixed charges and giant graviton numbers $n_I$
by a saddle point analysis, and further maximize it in $n_I$. This agrees with
the dual black hole entropy in the small black hole limit. To get black holes
at general sizes, one should note that various giant graviton indices cancel
because gauge theory does not suffer from a Hagedorn-like pathology by an
infinite baryonic tower. With one assumption on the mechanism of this
cancellation, we account for the dual black hole entropy at general sizes. We
interpret our results as analytic continuations of the large $N$ free energies
of SCFTs, and based on it compute the entropies of AdS$_{4,7}$ black holes from
M5, M2 giant gravitons.
