The microquasar LS 5039 has recently been detected as a source of very high energy (VHE) γ-rays. This detection, that confirms the previously proposed association of LS 5039 with the EGRET source 3EG J1824-1514, makes of LS 5039 a special system with observational data covering nearly all the electromagnetic spectrum. In order to reproduce the observed spectrum of LS 5039, from radio to VHE γ-rays, we have applied a cold matter dominated jet model that takes into account accretion variability, the jet magnetic field, particle acceleration, adiabatic and radiative losses, microscopic energy conservation in the jet, and pair creation and absorption due to the external photon fields, as well as the emission from the first generation of seconda...