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 +/- 0.09 M_sun with a dispersion of sigma = 0.21 +/- 0.09. Neutron stars with masses in excess of 2 M_sun are consistent with, but not firmly demanded by, current observations. Redback companions have median masses of 0.36 +/- 0.04 M_sun with a scatter of sigma = 0.15 +/- 0.04, and a tail possibly extending up to 0.7-0.9 M_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 spindown energy to gamma-ray luminosity is ~10%.
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