  We present deep Spitzer 3.6 micron observations of three z~5 GRB host
galaxies. Our observations reveal that z~5 GRB hosts are a factor of 3 less
luminous than the median rest-frame V-band luminosity of spectroscopically
confirmed z~5 galaxies in the GOODS fields and the UDF. The strong connection
between GRBs and massive star formation implies that not all star-forming
galaxies at these redshifts are currently being accounted for in deep surveys
and GRBs provide a unique way to measure the contribution to the star-formation
rate density from galaxies at the faint end of the galaxy luminosity function.
By correlating the co-moving star-formation rate density with co-moving GRB
rates at lower redshifts, we estimate a lower limit to the star-formation rate
density of 0.12+/-0.09 and 0.09+/-0.05 M_sun/yr/Mpc^3 at z~4.5 and z~6,
respectively. Finally, we provide evidence that the average metallicity of
star-forming galaxies evolves as (stellar mass density)^(0.69+/-0.17) between
$z\sim5$ and $z\sim0$, probably indicative of the loss of a significant
fraction of metals to the intergalactic medium, particularly in low-mass
galaxies.
