We present a broadband X-ray spectral analysis of the M51 system, including the dual active galactic nuclei (AGN) and several off-nuclear point sources. Using a deep observation by NuSTAR, new high-resolution coverage of M51b by Chandra, and the latest X-ray torus models, we measure the intrinsic X-ray luminosities of the AGN in these galaxies. The AGN of M51a is found to be Compton thick, and both AGN have very low accretion rates ($lambda_{rm Edd} <10^{-4}$). The latter is surprising considering that the galaxies of M51 are in the process of merging, which is generally predicted to enhance nuclear activity. We find that the covering factor of the obscuring material in M51a is $0.26 pm 0.03$, consistent with the local AGN obscured fraction at $L_{rm X}sim 10^{40}$ erg s$^{-1}$. The substantial obscuring column does not support theories that the torus, presumed responsible for the obscuration, disappears at these low accretion luminosities. However, the obscuration may have resulted from the gas infall driven by the merger rather than the accretion process. We report on several extra-nuclear sources with $L_{rm X}>10^{39}$ erg s$^{-1}$ and find that a spectral turnover is present below 10 keV in most such sources, in line with recent results on ultraluminous X-ray sources.