Context.LS 5039 is one of the few TeV emitting X-ray binaries detected so far. The powering source of its multiwavelength emission can be accretion in a microquasar scenario or wind interaction in a young nonaccreting pulsar scenario. Aims.To present new high-resolution radio images and compare them with the expected behavior in the different scenarios. Methods.We analyze Very Long Baseline Array (VLBA) radio observations that provide morphological and astrometric information at milliarcsecond scales. Results.We detect a changing morphology between two images obtained five days apart. In both runs there is a core component with a constant flux density, and an elongated emission with a position angle (PA) that changes by 12 ± $3\degr$ between both runs. The source is nearly symmetric in the first run and asymmetric in the second one. The astrometric results are not conclusive. Conclusions.A simple and shockless microquasar scenario cannot easily explain the observed changes in morphology. An interpretation within the young nonaccreting pulsar scenario requires the inclination of the binary system to be very close to the upper limit imposed by the absence of X-ray eclipses.