We present new optical - near-IR spectroscopic and photometric observations of the newly discovered galactic microquasar LS 5039, which indicate a classification for the mass donor in the system of O6.5V((f)). Optical spectroscopy and photometry shows no variability over a timescale of years, and we find no evidence of modulation by, or emission from the compact companion in these data. However significant photometric variability ( ~0.4 mag) is present in the H and K bands between 1995-2000. Such variability has been observed in other radio bright X-ray binaries where it has been attributed to synchrotron emission from the jet. However, given the non-thermal spectral index of the radio emission in LS 5039 this explanation appears unlikely, predicting a near-IR flux ~ 3 orders of magnitude too small to contribute significantly at such wavelengths. Nightly optical photometry over a 21 day period between 2000 May-June reveals variability at a level of a few hundredths of a magnitude, with no periodicity or long term trend visible. Likewise, while the radio lightcurves show moderate variability ( ~20 per cent of the mean flux density) we find no evidence of periodic modulation - Monte Carlo simulations constrain any such periodic variability to <4 per cent modulation at 2.25 GHz. The differences in behaviour between LS 5039 and Cygnus X-1 - the most closely related radio emitting High Mass X-ray Binary - are likely to be a result of the weaker stellar wind and probable greater orbital separation of LS 5039 compared to Cyg X-1.