Aims. LS 5039 is an enigmatic high-mass gamma-ray binary which hosts a powerful O6.5V companion, while the nature of the compact object is still to be established by multi-wavelength observations analysis. Methods. Phase-resolved multi-instrument spectra of nonthermal emission from LS 5039 are analyzed in order to produce reliable spectral models, which can be further employed to select between various scenarios and theoretical models of the binary.Results. The combined phase-resolved hard X-ray and MeV-range gamma-ray spectra obtained with XMM-Newton, Suzaku, NuSTAR, INTEGRAL, and COMPTEL indicate a meaningful spectral hardening above 50 keV. The spectral break observed in both major phases of the binary may indicate the presence of two populations of accelerated leptons in the emitting region, which could originate from the collision of the O6.5V companion star wind with the flow from yet unidentified compact object.