We construct spinning black hole solutions in five dimensions that take into account the mixed gauge-gravitational Chern-Simons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a Taub-NUT base space in order to test recent conjectures relating 5D black holes to 4D black holes and the topological string. Our explicit results show that certain charge shifts have to be taken into account for these relations to hold. We also compute corrections to the entropy of black rings in terms of near horizon data.
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