G347.3-0.5 (RX J1713.7-3946) is a member of the new class of shell-type Galactic supernova remnants (SNRs) that feature non-thermal components to their X-ray emission. We have analyzed the X-ray spectrum of this SNR over a broad energy range (0.5 to 30 keV) using archived data from observations made with two satellites, the Roentgenstaellit (ROSAT) and the Advanced Satellite for Cosmology and Astrophysics (ASCA), along with data from our own observations made with the Rossi X-ray Timing Explorer (RXTE). Using a combination of the models EQUIL and SRCUT to fit thermal and non-thermal emission, respectively, from this SNR, we find evidence for a modest thermal component to G347.3-0.5s diffuse emission with a corresponding energy of kT = 1.4 keV. We also obtain an estimate of 70 TeV for the maximum energy of the cosmic-ray electrons that have been accelerated by this SNR.