Our analysis of a 24 ks ROSAT Position Sensitive Proprtional Counter (PSPC) image of the interacting galaxies NGC 5194 (M51) and NGC 5195 shows that X-ray emission is distributed across the whole of NGC 5194. In addition to the diffuse emission and a bright nuclear region, eight individual sources were detected with 0.2-2.2 keV luminosities from 5 to 29 x 10(exp 38) ergs/s, more than 10 times higher than typical bright Galactic X-ray sources. The energy distribution of the luminous sources can be characterized by bremsstrahlung spectra with temperatures around 1 keV and low-energy absorption exceeding that expected from our Galaxy. Two sources lie in an inner spiral arm, while five lie along the outer edges of the outer spiral arms. Four sources (R1, R2, R4, R6) lie in or near regions of recent star formation as indicated by H II regions or CO emission from molecular clouds. However, for three of the X-ray sources which fall on the outer edge of the spiral arms (R3, R7, and R8), there is little or no associated CO or H alpha emission. We discuss the origin of the luminous X-ray sources as possibly arising from either massive black holes in binary star systems, supernova remnants, or hot gas associated with star forming regions.