We present deep 3.6 \mu m observations of three z \sim 5 GRB host galaxies with the Spitzer Space Telescope .
The host of GRB 060510B , at z = 4.942 , is detected with a flux density of 0.23 \pm 0.04 \mu Jy , corresponding to a rest-frame V - band luminosity of 1.3 \times 10 ^ { 10 } L _ { \sun } , or \approx 0.15 L _ { *, { V } ,z = 3 } .
We do not detect the hosts of GRBs 060223A and 060522 and constrain their rest-frame V - band luminosity to < 0.1 L _ { *, { V } ,z = 3 } .
Our observations reveal that z \sim 5 GRB host galaxies are a factor of \sim 3 less luminous than the median luminosity of spectroscopically-confirmed z \sim 5 galaxies in the Great Observatories Origins Deep Survey ( GOODS ) and the Hubble Ultra Deep Field ( 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 \pm 0.09 and 0.09 \pm 0.05 M _ { \sun } yr ^ { -1 } Mpc ^ { -3 } at z \sim 4.5 and z \sim 6 , respectively .
This is in excellent agreement with extinction corrected estimates from Lyman-break galaxy samples .
Finally , our observations provide initial evidence that the metallicity of star-forming galaxies evolve more slowly than the stellar mass density between z \sim 5 and z \sim 0 , probably indicative of the loss of a significant fraction of metals to the intergalactic medium , especially in low-mass galaxies .