  We present broad-band, multi-epoch X-ray spectroscopy of the pulsating
ultra-luminous X-ray source (ULX) in NGC 5907. Simultaneous XMM-Newton and
NuSTAR data from 2014 are best described by a multi-color black-body model with
a temperature gradient as a function of accretion disk radius significantly
flatter than expected for a standard thin accretion disk (T(r) ~ r^{-p}, with
p=0.608^{+0.014}_{-0.012}). Additionally, we detect a hard power-law tail at
energies above 10 keV, which we interpret as being due to Comptonization. We
compare this observation to archival XMM-Newton, Chandra, and NuSTAR data from
2003, 2012, and 2013, and investigate possible spectral changes as a function
of phase over the 78d super-orbital period of this source. We find that
observations taken around phases 0.3-0.4 show very similar temperature
profiles, even though the observed flux varies significantly, while one
observation taken around phase 0 has a significantly steeper profile. We
discuss these findings in light of the recent discovery that the compact object
is a neutron star and show that precession of the accretion disk or the neutron
star can self-consistently explain most observed phenomena.
