We have discovered six galaxies with spectroscopically confirmed redshifts of 4.8<z<5.8 in a single 44 square arcminute field imaged deeply in R, I and z-bands. All the spectra show an emission-line in the region around 7000-8400 angstroms with a spectroscopically-detected faint continuum break across the line. These six were drawn from 13 sources with I_AB<26.2 and R_AB-I_AB>1.5 in the field, this photometric cut designed to select galaxies at z>4.8. The line fluxes range between 0.2 to 2.5 x 10^-17 ergs cm^-2 s^-1 indicating luminosities of around 10^42-43 ergs s^-1 for Ly-alpha and their high emission line equivalent widths suggest very young ages (<10^8 yrs). A further line-emitting object with no detectable continuum was serendipitously detected by spectroscopy. If this line is Ly-alpha then it is from a source at z=6.6, making this the most distant galaxy known. However, the redshift cannot be considered secure as it is based on a single line. No broad emission line objects (quasars) were detected. The 13 sources at I_AB<26.2 are less than that expected if the luminosity function of dropout galaxies remained unchanged between z=3 and z=6, although the deficit is not highly significant given possible cosmic variance. The UV luminosity density from galaxies brighter than our flux limit is considerably less than that necessary to keep the volume probed by our field at <z>~5.3 ionized. These galaxies are observed within several hundred Myr of the end of the epoch of reionization (z=6-7), with little time for the luminosity function to evolve. This, and the lack of detected quasars, imply that the bulk of the UV flux that reionized the universe came from faint galaxies with M_(1700 ang)>-21.