The properties of the orbit and the donor star in the high mass X-ray binary microquasar LS 5039 indicate that accretion processes should mainly occur via a radiatively driven wind. In such a scenario, significant X-ray variability would be expected due to the eccentricity of the orbit. The source has been observed at X-rays by several missions, although with a poor coverage that prevents to reach any conclusion about orbital variability. Therefore, we conducted RossiXTE observations of the microquasar system LS 5039 covering a full orbital period of 4 days. Individual observations are well fitted with an absorbed power-law plus a Gaussian at 6.7 keV, to account for iron line emission that is probably a diffuse background feature. In addition, we have taken into account that the continuum is also affected by significant diffuse background contamination. Our results show moderate power-law flux variations on timescales of days, as well as the presence of miniflares on shorter timescales. The new orbital ephemeris of the system recently obtained by Casares et al. have allowed us to show, for the first time, that an increase of emission is seen close to the periastron passage, as expected in an accretion scenario. Moreover, the detected orbital variability is a factor of ~4 smaller than the one expected by using a simple wind accretion model, and we suggest that an accretion disk around the compact object could be responsible for this discrepancy. On the other hand, significant changes in the photon index are also observed clearly anti-correlated with the flux variations. We interpret the overall X-ray spectral characteristics of LS 5039 in the context of X-ray radiation produced by inverse Compton and/or synchrotron processes in the jet of this microquasar.