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We study higher-order corrections to two BPS solutions of 5D supergravity,namely the supersymmetric black ring and the spinning black hole. Due in partto our current relatively limited understanding of F-type terms in 5Dsupergravity, the nature of these corrections is less clear than that of their4D cousins. Effects of certain $R^2$ terms found in Calabi-Yau compactificationof M-theory are specifically considered. For the case of the black ring, forwhich the microscopic origin of the entropy is generally known, thecorresponding higher order macroscopic correction to the entropy is found tomatch a microscopic correction, while for the spinning black hole thecorrections are partially matched to those of a 4D $D0-D2-D6$ black hole.Comment: 9 page

R2corrections for 5D black holes and rings

R²corrections for 5D black holes and rings