We present a chemical composition analysis of 36 giant stars in the mildly metal-poor (< [Fe/H]> = -1.21) globular cluster M5 (NGC 5904). The analysis makes use of high-resolution data acquired for 25 stars at the Keck I telescope, as well as a reanalysis of the high-resolution spectra for 13 stars acquired for an earlier study at Lick Observatory. We employed two analysis techniques : (1) adopting standard spectroscopic constraints, including setting the surface gravity from the ionization equilibrium of iron, and (2) subsequent to investigating alternative approaches, adopting an analysis consistent with the non-LTE precepts as recently described by & Idiart. The abundance ratios we derive for Thevenin magnesium, silicon, calcium, scandium, titanium, vanadium, nickel, barium, and europium in M5 show no significant abundance variations, and the ratios are comparable to those of halo field stars. However, large variations are seen in the abundances of oxygen, sodium, and aluminum, the elements that are sensitive to proton-capture nucleosynthesis. These variations are well-correlated with the CN band strength index S(3839). Surprisingly, in M5 the dependence of the abundance variations on log g is in the opposite sense to that discovered in M13 by the Lick-Texas group where the relationship provided strong evidence in support of the evolutionary scenario. The present analysis of M5 giants does not necessarily rule out an evolutionary scenario, but it provides no support for it either. In comparing the abundances of M5 and M4 (NGC 6121), another mildly metal-poor (< [Fe/H]> = -1.08) globular cluster, we find that silicon, aluminum, barium, and lanthanum are overabundant in M4 with respect to that seen in M5, confirming and expanding the results of previous studies. In comparing the abundances between these two clusters and others having comparable metallicities, we find that the anticorrelations observed in M5 are similar to those found in more metal-poor clusters, M3, M10, and M13 (< [Fe/H]> = -1.5 to -1.6), whereas the behavior in M4 is more like that of the more metal-rich globular cluster M71 (< [Fe/H]> similar to -0.8). We conclude that among stars in Galactic globular clusters there is no definitive "single" value of [X/Fe] at a given [Fe/H] for at least some alpha -capture, odd-Z, and slow neutron-capture process elements, in this case, silicon, aluminum, barium, and lanthanum.
