We report on the results from Suzaku broadband X-ray observations of the galactic binary source LS 5039. The Suzaku data, which have continuous coverage of more than one orbital period, show strong modulation of the X-ray emission at the orbital period of this TeV gamma-ray emitting system. The X-ray emission shows a minimum at orbital phase ~0.1, close to the so-called superior conjunction of the compact object, and a maximum at phase ~0.7, very close to the inferior conjunction of the compact object. The X-ray spectral data up to 70 keV are described by a hard power law with a phase-dependent photon index which varies within Γ 1.45- 1.61. The amplitude of the flux variation is a factor of 2.5, but is significantly less than that of the factor ~8 variation in the TeV flux. Otherwise the two light curves are similar, but not identical. Although periodic X-ray emission has been found from many galactic binary systems, the Suzaku result implies a phenomenon different from the "standard" origin of X-rays related to the emission of the hot accretion plasma formed around the compact companion object. The X-ray radiation of LS 5039 is likely to be linked to very high energy electrons which are also responsible for the TeV gamma-ray emission. While the gamma rays are the result of inverse Compton (IC) scattering by electrons on optical stellar photons, X-rays are produced via synchrotron radiation. Yet, while the modulation of the TeV gamma-ray signal can be naturally explained by the photon-photon pair production and anisotropic IC scattering, the observed modulation of synchrotron X-rays requires an additional process, the most natural one being adiabatic expansion in the radiation production region.