We present abundance measurements of elements O, C, Si and Fe for three gas-rich galaxies at z∼5 using observations from the Very Large Telescope (VLT) and the Keck telescope in order to better constrain the early chemical enrichment of gas-rich galaxies. These galaxies show strong Lyman-α absorption in the spectra of background quasars, with neutral hydrogen column densities log N H I (cm −2 ) = 20.10±0.15, 20.10±0.15, and 20.80±0.15. Using the undepleted element O, we find the metallicities [O/H] to be in the range of −2.51 to −2.05 dex. Our study has doubled the existing sample of measurements of undepleted elements at z > 4.5. Combining our measurements with those from the literature, we find that the N H I -weighted mean metallicity of z∼5 absorbers is consistent with the prediction based on z < 4.5 DLAs. Thus, we find no significant evidence of a sudden drop in metallicity at z > 4.7 as reported by some prior studies. We also determine the extent of dust depletion using a combination of both the volatile element O and the refractory elements Si and/or Fe. Some of the absorbers show evidence of depletion of elements on dust grains, e.g. low [Si/O] or [Fe/O]. The relative abundances of these absorbers along with other z∼5 absorbers from the literature show some peculiarities, e.g. low [C/O] in several absorbers and high [Si/O] in one absorber. Finally, we find that the metallicity vs. velocity dispersion relation of z∼5 absorbers may be different from that of lower-redshift absorbers.