The high-energy emission from nearby, star-forming galaxies is dominated by X-ray binaries, where a neutron star or black hole is accreting mass from either a low-mass (<~M_{sun}_) or high-mass (>~8M_{sun}_) star. Donor stars with intermediate masses ~3-7M_{sun}_ are also possible, but rarer in our Galaxy. Since it is not possible to separate low-, intermediate-, and high-mass X-ray binaries (LMXBs, IMXBs, and HMXBs) from their X-ray properties alone, we use optical images of M101 taken with the Hubble Space Telescope to directly constrain the masses of donor stars in X-ray binaries down to ~3M_{sun}_. For X-ray binaries that still live within their parent star cluster, the age of the cluster provides strong constraints on the mass of the donor and hence type of binary. We present the classification, on a source-by-source basis, of 140 X-ray point sources in the nearby spiral galaxy M101 (D=6.4+/-0.2Mpc). We find that, overall, HMXBs appear to follow the spiral arms, while LMXBs dominate the bulge region as expected, but also appear to form an inter-arm disk population. The X-ray luminosity functions for HMXBs and LMXBs are well fit by a power-law distribution, dN/dL_X_{propto}L^{alpha}^, with {alpha}=-1.71+/-0.06 (HMXBs) and {alpha}=-1.96+/-0.08 (LMXBs), and the brightest sources are consistent with the expectations from sampling statistics without requiring a physical cutoff. Overall, our results for HMXB and LMXB populations agree well with the specific star formation rate map presented for M101 recently by Lehmer and collaborators.