  With optical and near-infrared follow-up observations of gamma-ray bursts
(GRBs) it is possible to study the chemical enrichment of galaxies at high
redshift. Especially interesting are measurements of the metallicity of GRB
host with $z\gtrsim 4.7$, since it has recently been shown that damped
Lymann-$\alpha$ absorbers have a rapid decrease in metallicity at this redshift
(Rafelski et al. 2013). In this paper measurements of the amount of metals and
dust in the host galaxy of GRB 111008A at $z=5.0$ is presented, and it is
discussed how observations of more high-$z$ GRB host galaxies can give clues
about dust formation mechanisms and the distribution of metals in the early
Universe.
