We discovered eclipses and dips in two luminous ( and highly variable ) X-ray sources in M 51 . One ( CXOM51 J132943.3 + 471135 ) is an ultraluminous supersoft source , with a thermal spectrum at a temperature of about 0.1 keV and characteristic blackbody radius of about 10 ^ { 4 } km . The other ( CXOM51 J132946.1 + 471042 ) has a two-component spectrum with additional thermal-plasma emission ; it approached an X-ray luminosity of 10 ^ { 39 } erg s ^ { -1 } during outbursts in 2005 and 2012 . From the timing of three eclipses in a series of Chandra observations , we determine the binary period ( 52.75 \pm 0.63 hr ) and eclipse fraction ( 22 \% \pm 0.1 \% ) of CXOM51 J132946.1 + 471042 . We also identify a blue optical counterpart in archival Hubble Space Telescope images , consistent with a massive donor star ( mass of \sim 20– 35 M _ { \odot } ) . By combining the X-ray lightcurve parameters with the optical constraints on the donor star , we show that the mass ratio in the system must be M _ { 2 } / M _ { 1 } \ga 18 , and therefore the compact object is most likely a neutron star ( exceeding its Eddington limit in outburst ) . The general significance of our result is that we illustrate one method ( applicable to high-inclination sources ) of identifying luminous neutron star X-ray binaries , in the absence of X-ray pulsations or phase-resolved optical spectroscopy . Finally , we discuss the different X-ray spectral appearance expected from super-Eddington neutron stars and black holes at high viewing angles .