  Under the assumption that LS 5039 is a system composed by a pulsar rotating
around an O6.5V star in a $\sim 3.9$ day orbit, we present the results of a
theoretical modeling of the high energy phenomenology observed by the High
Energy Stereoscopy Array (H.E.S.S.). This model (including detailed account of
the system geometry, Klein-Nishina inverse Compton, $\gamma$-$\gamma$
absorption, and cascading) is able to describe well the rich observed
phenomenology found in the system at all timescales, both flux and
spectrum-wise.
