We present here new observations conducted with the EVN and MERLIN of the persistent microquasar LS 5039 discovered by Paredes et al. (2000) with the VLBA. The new observations confirm the presence of an asymmetric two-sided jet reaching up to 1000 AU on the longest jet arm. The results suggest a bending of the jets with increasing distance from the core and/or precession. The origin and location of the high-energy gamma-ray emission associated with the system is discussed and an estimate of the magnetic field at the base of the jet given. Our results suggest a well collimated radio jet. We also comment on new observing strategies to be used with satellites and forthcoming detectors, since this persistent source appears to be a rather good laboratory to explore the accretion/ejection processes taking place near compact objects.