  We present Herschel PACS and SPIRE spectroscopy of the most important
far-infrared cooling lines in M51, [CII](158 \mu m), [NII](122 & 205 \mu m),
[OI](63 and 145 \mu m) and [OIII](88 \mu m). We compare the observed flux of
these lines with the predicted flux from a photon dominated region model to
determine characteristics of the cold gas such as density, temperature and the
far-ultraviolet radiation field, G_0, resolving details on physical scales of
roughly 600 pc. We find an average [CII]/F_TIR of 4 x 10^{-3}, in agreement
with previous studies of other galaxies. A pixel-by-pixel analysis of four
distinct regions of M51 shows a radially decreasing trend in both the
far-ultraviolet (FUV) radiation field, G_0 and the hydrogen density, n, peaking
in the nucleus of the galaxy, then falling off out to the arm and interarm
regions. We see for the first time that the FUV flux and gas density are
similar in the differing environments of the arm and interarm regions,
suggesting that the inherent physical properties of the molecular clouds in
both regions are essentially the same.
