  LS 5039 is so far the best studied $\gamma$-ray binary system at
multi-wavelength energies. A time resolved study of its spectral energy
distribution (SED) shows that above 1 keV its power output is changing along
its binary orbit as well as being a function of energy. To disentangle the
energy dependence of the power output as a function of orbital phase, we
investigated in detail the orbital light curves as derived with different
telescopes at different energy bands. We analysed the data from all existing
\textit{INTEGRAL}/IBIS/ISGRI observations of the source and generated the most
up-to-date orbital light curves at hard X-ray energies. In the $\gamma$-ray
band, we carried out orbital phase-resolved analysis of \textit{Fermi}-LAT data
between 30 MeV and 10 GeV in 5 different energy bands. We found that, at
$\lesssim$100 MeV and $\gtrsim$1 TeV the peak of the $\gamma$-ray emission is
near orbital phase 0.7, while between $\sim$100 MeV and $\sim$1 GeV it moves
close to orbital phase 1.0 in an orbital anti-clockwise manner. This result
suggests that the transition region in the SED at soft $\gamma$-rays (below a
hundred MeV) is related to the orbital phase interval of 0.5--1.0 but not to
the one of 0.0--0.5, when the compact object is "behind" its companion. Another
interesting result is that between 3 and 20 GeV no orbital modulation is found,
although \textit{Fermi}-LAT significantly ($\sim$18$\sigma$) detects LS 5039.
This is consistent with the fact that at these energies, the contributions to
the overall emission from the inferior conjunction phase region (INFC, orbital
phase 0.45 to 0.9) and from the superior conjunction phase region (SUPC,
orbital phase 0.9 to 0.45) are equal in strength. At TeV energies the power
output is again dominant in the INFC region and the flux peak occurs at phase
$\sim$0.7.
