  We study four-derivative corrections to five-dimensional minimal gauged
supergravity. We evaluate the on-shell action of the AdS$_5$ black hole
solution with two independent angular momenta and one electric charge at linear
order in the corrections. After imposing supersymmetry, we are able to recast
the action in terms of the supersymmetric chemical potentials and match the
result obtained from the dual superconformal index on the second sheet. To
achieve this, we exploit the freedom to implement field redefinitions to recast
the action in a much simpler form, as well as the fact that the two-derivative
solution is enough. We use the on-shell action to determine the corrections to
the black hole thermodynamics, including those to the entropy and the charges.
We then specialize to the supersymmetric and extremal case and find a simple
expression for the microcanonical entropy. In particular, for the case with one
independent angular momentum the corrections are entirely encoded in the dual
superconformal anomaly coefficients. We corroborate this result for the entropy
by constructing the corrected near-horizon solution and applying Wald's
formula.
