  The possible association between the microquasar LS 5039 and the EGRET source
3EG J1824-1514 suggests that microquasars could also be sources of high energy
gamma-rays. In this paper, we explore, with a detailed numerical model, if this
system can produce the emission detected by EGRET (>100 MeV) through inverse
Compton (IC) scattering. Our numerical approach considers a population of
relativistic electrons entrained in a cylindrical inhomogeneous jet,
interacting with both the radiation and the magnetic fields, taking into
account the Thomson and Klein-Nishina regimes of interaction. The computed
spectrum reproduces the observed spectral characteristics at very high energy.
