We report millimeter-sized Nd5Pb3 single crystals grown out of a Nd-Co flux. We experimentally study the magnetic order of Nd5Pb3 single crystals by measuring the anisotropic magnetic properties, electrical resistivity under high pressure up to 8 GPa, specific heat, and neutron single crystal diffraction. Two successive magnetic orders are observed at T N1 = 44 K and T N2 = 8 K. The magnetic cells can be described with a propagation vector [Formula: see text]. Cooling below T N1, Nd1 and Nd3 order forming ferromagnetic stripes along the b-axis, and the ferromagnetic stripes are coupled antiferromagnetically along the a-axis for the [Formula: see text] magnetic domain. Cooling below T N2, Nd2 orders antiferromagnetically to nearby Nd3 ions. All ordered moments align along the crystallographic c-axis. The magnetic order at T N1 is accompanied by a quick drop of electrical resistivity upon cooling and a lambda-type anomaly in the temperature dependence of specific heat. At T N2, no anomaly was observed in electrical resistivity but there is a weak feature in specific heat. The resistivity measurements under hydrostatic pressures up to 8 GPa suggest a possible phase transition around 6 GPa. Our first-principles band structure calculations show that Nd5Pb3 has the same electronic structure as does Y5Si3 which has been reported to be a one-dimensional electride with anionic electrons that do not belong to any atom. Our study suggests that R 5Pb3 (R = rare earth) can be a materials playground for the study of magnetic electrides. This deserves further study after experimental confirmation of the presence of anionic electrons.