  We study four-derivative corrections to 5d $\mathcal{N}=2$ minimal gauged
supergravity using tools from conformal supergravity. There are two
supersymmetric invariants at the four-derivative order and we show explicitly
how to write down the action in the Poincar\'{e} frame in terms of their
coefficients. We apply our results in the context of holography where the
four-derivative terms in the supergravity action translate into corrections to
the conformal anomalies of the dual 4d $\mathcal{N}=1$ SCFT. We use these
results to study corrections to the entropy of the supersymmetric black string
solutions of minimal supergravity. We also discuss explicit embeddings of the
5d supergravity in string and M-theory and use them to fix the
higher-derivative coefficients in terms of the microscopic parameters.
