Global well-posedness for the fifth-order KdV equation in H^-1(R) We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in H^-1(R). Global well-posedness in L^2(R) was shown previously in [8] using the method of commuting flows. Since this method is insensitive to the ambient geometry, it cannot go beyond the sharp L^2 threshold for the torus demonstrated in [3]. To prove our result, we introduce a new strategy that integrates dispersive effects into the method of commuting flows. 7 2 Springer Nature