We present the first optical spectroscopy of five confirmed (or strong candidate) redback millisecond pulsar binaries, obtaining complete radial velocity curves for each companion star. The properties of these millisecond pulsar binaries with low-mass, hydrogen-rich companions are discussed in the context of the 14 confirmed and 10 candidate field redbacks. We find that the neutron stars in redbacks have a median mass of 1.78+/-0.09M_{sun}_ with a dispersion of {sigma}=0.21+/-0.09. Neutron stars with masses in excess of 2M_{sun}_ are consistent with, but not firmly demanded by, current observations. Redback companions have median masses of 0.36+/-0.04M_{sun}_ with a scatter of {sigma}=0.15+/-0.04M_{sun}_, and a tail possibly extending up to 0.7-0.9M_{sun}_. Candidate redbacks tend to have higher companion masses than confirmed redbacks, suggesting a possible selection bias against the detection of radio pulsations in these more massive candidate systems. The distribution of companion masses between redbacks and the less massive black widows continues to be strongly bimodal, which is an important constraint on evolutionary models for these systems. Among redbacks, the median efficiency of converting the pulsar spin-down energy to {gamma}-ray luminosity is ~10%.