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In this paper we investigate the attractor mechanism in the five dimensionallow energy supergravity theory corresponding to M-theory compactified on aCalabi-Yau threefold $CY_3$. Using very special geometry, we derive the generalfirst-order attractor flow equations for BPS and non-BPS solutions infive-dimensional Gibbons-Hawking spaces. Especially, considering thesupersymmetric solution, we obtain the first-order flow equations forsupersymmetric (multi)black rings. We also solve the flow equations and discusssome properties of the solutions of flow equations.

First-order attractor flow equations for supersymmetric black rings in N=2, D=5 supergravity