Before revision:  Our main technical contribution is to prove 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 via a deterministic algorithm , which is a result of independent interest .
After revision:  Our main technical contribution is to prove 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 we obtain the currently best deterministic algorithm for list-coloring random hypergraphs of bounded average degree .