  We evaluate the large-$N$ behavior of the superconformal indices of toric
quiver gauge theories, and use it to find the entropy functions of the dual
electrically charged rotating $\mathrm{AdS}_5$ black holes. To this end, we
employ the recently proposed Bethe Ansatz method, and find a certain set of
solutions to the Bethe Ansatz Equations of toric theories. This, in turn,
allows us to compute the large-$N$ behavior of the index for these theories,
including the infinite families $Y^{pq}$, $X^{pq}$ and $L^{pqr}$ of quiver
gauge theories. Our results are in perfect agreement with the predictions made
recently using the Cardy-like limit of the superconformal index. We also
explore the index structure in the space of chemical potentials and describe
the pattern of Stokes lines arising in the conifold theory case.
