We present results from direct measurements of the thick-target yield from laboratory incident energies 3 to 5 MeV, performed with the 3HeBF3 Giant Barrel (HeBGB) neutron detector at the Edwards Accelerator Laboratory. Our measurements have a small energy cadence in order to address discrepancies and sparseness of thick-target-yield data sets existing for this energy region. We find general agreement with existing data sets, including yields derived from cross-section data, while resolving a discrepancy between existing thick-target-yield data sets for  MeV. However, for  MeV, our results are substantially lower than previous thick-target-yield data and somewhat larger than yields calculated from existing cross-section data. Our data complete the energy range needed for estimates of the contribution to neutrino and dark matter detector backgrounds and result in increased viability of as a plasma diagnostic tool at fusion facilities such as the National Ignition Facility.