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We present here the results of the timing of PSR B1516+02B, a 7.95‐ms pulsar in a binary system with a $∼0.17M⊙$ companion and an orbital period of 6.85 days located in the globular cluster M5. The eccentricity of the orbit $(e = 0.14)$ has allowed a measurement of the rate of advance of periastron: $ω̇ = (0.0136±0.0004)° yr−1.$ It is very likely that the periastron advance is due to the effects of general relativity; the total mass of the binary system is $(2.14±0.08)M⊙.$ The small measured mass function implies, in a statistical sense, that a very large fraction of this total mass is contained in the pulsar: $Mp = (1.95−0.12+0.09)M⊙$ (68% probability); there is a 5% probability that the mass of this object is below $1.68M⊙.$ With the possible exception of PSR J1748–2021B, this is the largest neutron star mass measured to date. When combined with similar measurements made previously for Terzan 5 I and J, we can exclude, in a statistical sense, the “soft” equations of state for dense neutron matter, implying that matter at the center of a neutron star is highly incompressible. We also discuss a possible anti‐correlation between spin period and pulsar mass, and discuss its possible significance in terms of the formation mechanisms of millisecond pulsars.