  We present new measurements of the mean transmitted flux in the Ly-alpha
forest over 2 < z < 5 made using 6065 quasar spectra from the Sloan Digital Sky
Survey DR7. We exploit the general lack of evolution in the mean quasar
continuum to avoid the bias introduced by continuum fitting over the Ly-alpha
forest at high redshifts, which has been the primary systematic uncertainty in
previous measurements of the mean Ly-alpha transmission. The individual spectra
are first combined into twenty-six composites with mean redshifts spanning 2.25
< z_comp < 5.08. The flux ratios of separate composites at the same rest
wavelength are then used, without continuum fitting, to infer the mean
transmitted flux, F(z), as a fraction of its value at z~2. Absolute values for
F(z) are found by scaling our relative values to measurements made from
high-resolution data by Faucher-Giguere et al. (2008) at z < 2.5, where
continuum uncertainties are minimal. We find that F(z) evolves smoothly with
redshift, with no evidence of a previously reported feature at z~3.2. This
trend is consistent with a gradual evolution of the ionization and thermal
state of the intergalactic medium over 2 < z < 5. Our results generally agree
with the most careful measurements to date made from high-resolution data, but
offer much greater precision and extend to higher redshifts. This work also
improves upon previous efforts using SDSS spectra by significantly reducing the
level of systematic error.
