  We present an analysis of a large sample of moderate resolution Keck LRIS
spectra of subgiant (V \sim 17.2) and fainter stars in the Galactic globular
cluster M5 (NGC 5904) with the goal of deriving C and N abundances.
Star-to-star stochastic variations with significant range in both [C/Fe] and
[N/Fe] are found at all luminosities extending to the bottom of the RGB at M_V
\sim +3. Similar variations in CH appear to be present in the main sequence
turnoff spectra. There is no sign of a change in the behavior of C and N with
evolutionary stage over the full range in luminosity of the RGB and SGB. The C
and N abundances appear strongly anti-correlated, as would be expected from the
CN-cycle processing of stellar material. Yet the present stars are considerably
fainter than the RGB bump, the point at which deep mixing is believed to set
in. On this basis, while the observed abundance pattern is consistent with
proton capture nucleosynthesis, we infer that the site of the reactions is
likely not within the present sample, but rather in a population of more
massive (2 -- 5 M(Sun)) now defunct stars. The range of variation of the N
abundances is very large and the sum of C+N increases as C decreases. To
reproduce this requires the incorporation not only of CN but also of
ON-processed material. Furthermore, the existence of this correlation is quite
difficult to reproduce with an external mechanism such as ``pollution'' with
material processed in a more massive AGB star, which mechanism is fundamentally
stochastic in nature. We therefore suggest that although the internal mixing
hypothesis has serious flaws,new theoretical insights are needed and it should
not be ruled out yet. (abridged)
