  We show that, for every $k \ge 2$, every $k$-uniform hypergaph of degree
$\Delta$ and girth at least $5$ is efficiently $(1+o(1) )(k-1) (\Delta / \ln
\Delta )^{ 1/(k-1) } $-list colorable. As an application (and to the best of
our knowledge) we obtain the currently best algorithm for list-coloring random
hypergraphs of bounded average degree.
