We describe the analysis of the seven broad-band X-ray continuum observations of the archetypal Seyfert 1 galaxy NGC 5548 that were obtained with XMM-Newton or Chandra, simultaneously with high-energy (> 10 keV) observations with NuSTAR and INTEGRAL. These data were obtained as part of a multiwavelength campaign undertaken from the summer of 2013 till early 2014. We find evidence of a high-energy cut-off in at least one observation, which we attribute to thermal Comptonization, and a constant reflected component that is likely due to neutral material at least a few light months away from the continuum source. We confirm the presence of strong, partial covering X-ray absorption as the explanation for the sharp decrease in flux through the soft X-ray band. The obscurers appear to be variable in column density and covering fraction on time scales as short as weeks. A fit of the average spectrum over the range 0.3-400 keV with a realistic Comptonization model indicates the presence of a hot corona with a temperature of 40(+40,-10) keV and an optical depth of 2.7(+0.7,-1.2) if a spherical geometry is assumed.
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