We report relative measurements of the n(vector sign)-d(vector sign) longitudinal spin-dependent total cross-section difference ({delta}{sigma}{sub L}){sub d}, at E{sub n}(lab) = 5.0, 6.88, and 9.0 MeV. The deuteron target was polarized via dynamic nuclear polarization at 250 mK in a 2.5-T external magnetic field. The target polarization was monitored by nuclear magnetic resonance and was calibrated by a ({delta}{sigma}{sub L}){sub d} measurement at E{sub n}(lab) = 1.18 MeV. The polarized neutron beams were produced through the {sup 3}H(p(vector sign),n(vector sign)){sup 3}He and {sup 2}H(d(vector sign),n(vector sign)){sup 3}He reactions. The neutron polarizations were determined either by direct measurement or from known or calculated polarization-transfer coefficients. The results for ({delta}{sigma}{sub L}){sub d} show agreement with theoretical calculations based on nucleon-nucleon potential models but are not of sufficient precision to distinguish the presence or absence of three-nucleon force contributions to the cross sections.