The detection efficiency of a large cylindrical block of NE-12 scintillator was measured for neutrons with energies from 2 to 5 MeV. The experimental technique employed quasi-free p-n and p-p scattering from p-d breakup at 8 MeV and relied on the spectator model description of these processes. The measured efficiencies are 15% to 4% larger than the best calculated efficiencies and show an increasing deviation with neutron energy. The observed discrepancies are explained in terms of nuclear in-scattering and possible deficiencies in the spectator model. Several changes in the experimental apparatus and technique are suggested to improve the efficiency measurement.