We report the results of 19 years of Arecibo timing for two pulsars in the globular cluster NGC 5904 ( M5 ) , PSR B1516+02A ( M5A ) and PSR B1516+02B ( M5B ) . This has resulted in the measurement of the proper motions of these pulsars and , by extension , that of the cluster itself . M5B is a 7.95-ms pulsar in a binary system with a > 0.13 M _ { \sun } companion and an orbital period of 6.86 days . In deep HST images , no optical counterpart is detected within \sim 2.5 \sigma of the position of the pulsar , implying that the companion is either a white dwarf or a low-mass main-sequence star . The eccentricity of the orbit ( e = 0.14 ) has allowed a measurement of the rate of advance of periastron : \dot { \omega } = ( 0.0142 \pm 0.0007 ) ^ { \circ } yr ^ { -1 } . We argue that it is very likely that this periastron advance is due to the effects of general relativity , the total mass of the binary system then being ( 2.29 \pm 0.17 ) M _ { \sun } . The small measured mass function implies , in a statistical sense , that a very large fraction of this total mass is contained in the pulsar : M _ { p } = ( 2.08 \pm 0.19 ) M _ { \sun } ( 1 \sigma ) ; there is a 5 % probability that the mass of this object is < 1.72 M _ { \sun } and a 0.77 % probability that 1.2 M _ { \sun } \leq M _ { p } \leq 1.44 M _ { \sun } . Confirmation of the median mass for this neutron star would exclude most “ soft ” equations of state for dense neutron matter . Millisecond pulsars ( MSPs ) appear to have a much wider mass distribution than is found in double neutron star systems ; about half of these objects are significantly more massive than 1.44 M _ { \sun } . A possible cause is the much longer episode of mass accretion necessary to recycle a MSP , which in some cases corresponds to a much larger mass transfer .