  We report on detailed analysis of the hard X-ray and GeV gamma-ray spectra of
LS 5039, one of the brightest gamma-ray binary system in the Galaxy. The NuSTAR
observation covering its entire orbit in 2016 allowed us for the first time to
study the orbital variability of the spectrum above 10 keV. The hard X-ray
spectrum is well described with a single power-law component up to 78 keV. The
X-ray flux showed a slight deviation from those observed previously with Suzaku
in 2007. The fast X-ray brightening observed with Suzaku, around the inferior
conjunction, was not observed in this observation. We also analyzed 11 years of
Fermi Large Area Telescope data of LS 5039. The GeV spectrum around the
inferior conjunction was well described with two non-thermal components; a
power law with a photon index of $\sim 3$ and a cut-off power law with a cutoff
energy of $\sim 2$ GeV. The orbital flux variability also changed gradually
around a few GeV. These results indicate that there are two emission components
in the GeV band, and the dominant component above $\sim 1$ GeV does not depend
on the orbital phase. By combining these results, we update the spectral energy
distribution of LS 5039 with the highest available statistics. Theoretical
models proposed so far cannot explain the obtained multi-wavelength spectrum,
especially the emission from $\sim$ 1 MeV to $\sim$ 400 MeV, and we discuss a
possibility that particle acceleration in LS 5039 is different from the shock
acceleration.
