Microquasars are X-ray binaries with relativistic jets. The microquasar LS 5039 turned out to be the first high-energy gamma-ray microquasar candidate due to its likely association with the EGRET source 3EG J1824-1514. Further theoretical studies supported this association, which could be extended to other EGRET sources. Very recently, Aharonian et al. (2005) have communicated the detection of the microquasar LS 5039 at TeV energies. This fact confirms the EGRET source association and leaves no doubt about the gamma-ray emitting nature of this object. The aim of the present work is to show that, applying a cold-matter dominated jet model to LS 5039, we can reproduce many of the spectral and variability features observed in this source. Jet ...