Here we report the results of the first ever contemporaneous multi-wavelength observation campaign on the BL Lac object PKS 2155-304 involving Swift, NuSTAR, Fermi-LAT, and H.E.S.S. The use of these instruments allows us to cover a broad energy range, which is important for disentangling the different radiative mechanisms. The source, observed from June 2013 to October 2013, was found in a low flux state with respect to previous observations but exhibited highly significant flux variability in the X-rays. The high-energy end of the synchrotron spectrum can be traced up to 40 keV without significant contamination by high-energy emission. A one-zone synchrotron self-Compton model was used to reproduce the broadband flux of the source for all the observations presented here but failed for previous observations made in April 2013. A lepto-hadronic solution was then explored to explain these earlier observational results.