Context. LS 5039 is an X-ray binary that presents non-thermal radio emission. The radiation at ~5 GHz is quite steady and optically thin, consisting of a dominant core plus an extended jet-like structure. There is a spectral turnover around 1 GHz, and evidence of variability on timescales of 1 yr at 234 MHz. Aims. We investigate the radio emitter properties using the available broadband radio data, and assuming two possible scenarios to explain the turnover: free-free absorption in the stellar wind, or synchrotron self-absorption. Methods. We use the relationships between the turnover frequency, the stellar wind density, the emitter location, size and magnetic field, and the Lorentz factor of the emitting electrons, as well as a reasonable assumption regarding the energy budget, to infer the properties of the low-frequency radio emitter. Also, we put this information in context with the broadband radio data. Results. The location and size of the low-frequency radio emitter can be restricted to $\ga$few AU from the primary star, its magnetic field to ~3 $\times$ 10-3–1 G, and the electron Lorentz factors to ~$10{-}100$. The observed variability of the extended structures seen with VLBA would point to electron bulk velocities $\ga$3 $\times$ 108 cm s-1, whereas much less variable radiation at 5 GHz would indicate velocities for the VLBA core $\la$108 cm s-1. The emission at 234 MHz in the high state would mostly come from a region larger than the dominant broadband radio emitter. Conclusions. We suggest a scenario in which secondary pairs, created via gamma-ray absorption and moving in the stellar wind, are behind the steady broadband radio core, whereas the resolved jet-like radio emission would come from a collimated, faster, outflow.