  We prove global well-posedness of the fifth-order Korteweg-de Vries equation
on the real line for initial data in $H^{-1}(\mathbb{R})$. By comparison, the
optimal regularity for well-posedness on the torus is known to be
$L^2(\mathbb{R}/\mathbb{Z})$.
  In order to prove this result, we develop a strategy for integrating the
local smoothing effect into the method of commuting flows introduced previously
in the context of KdV. It is this synthesis that allows us to go beyond the
known threshold on the torus.
