  With our new Ca-CN-CH-NH photometry, we revisit the globular cluster (GC) M5.
We find that M5 is a mono-metallic GC with a small metallicity dispersion. Our
carbon abundances show that the $\sigma$[C/Fe] of the M5 CN-s population, with
depleted carbon and enhanced nitrogen abundances, is significantly large for a
single stellar population. Our new analysis reveals that the M5 CN-s population
is well described by the two stellar populations: the CN-s$_{\rm I}$, being the
major CN-s component, with the intermediate carbon and nitrogen abundance and
the CN-s$_{\rm E}$ with the most carbon-poor and nitrogen-rich abundance. We
find that the CN-s$_{\rm E}$ is significantly more centrally concentrated than
the others, while CN-w and CN-s$_{\rm I}$ have similar cumulative radial
distributions. The red giant branch bump $V$ magnitude, the helium abundance
barometer in mono-metallic populations, of individual populations appears to be
correlated with their mean carbon abundance, indicating that carbon abundances
are anticorrelated with helium abundances. We propose that the CN-s$_{\rm E}$
formed out of gas that experienced proton-capture processes at high
temperatures in the innermost region of the proto-GC of M5 that resided in a
dense ambient density environment. Shortly after, the CN-s$_{\rm I}$ formed out
of gas diluted from the pristine gas in the more spatially extended region,
consistent with the current development of numerical simulations by others.
