We present the iron abundance and abundance ratios for 18 elements with respect to Fe in a sample of stars with a wide range in luminosity, from luminous giants to stars near the turnoff in the globular cluster M5. The analyzed spectra, obtained with the High Resolution Echelle Spectrograph at the Keck Observatory, are of high dispersion (R = /D = 35,000). We find that the neutron capture, the iron peak, and the -element abundance ratios show no trend with T eff and low scatter around the mean between the top of the red giant branch and near the main-sequence turnoff, suggesting that at this metallicity non-LTE effects are not important over the range of stellar parameters spanned by our sample. To within the precision of the measurements (about AE0.1 dex), gravitationally induced heavy-element diffusion does not appear to be present among the stars near the main-sequence turnoff studied here. Our work and other recent studies suggest that heavy-element diffusion is inhibited in the surface layers of metal-poor stars. Differences in the Na abundance from star to star that extend to the main-sequence turnoff are detected in our sample in M5. The anticorrelation between O and Na abundances, observed in other metal-poor globular clusters, is not detected in our sample, but it may be hidden among stars with only upper limits for their O abundances. As we found in M71, there is a hint of star-to-star variation in the Zr abundance. Overall the abundance ratios of M5 appear very similar to those of M71, with the possible exception of the neutron capture element Ba, for which we argue that the apparent difference may be due to difficulties in the analysis. As in M71, the -elements Mg, Ca, Si, and Ti are overabundant relative to Fe. The results of our abundance analysis of 25 stars in M5 provide further evidence of abundance variations among specific light elements at unexpectedly low luminosities, which cannot be explained by our current understanding of stellar evolution.