Ternary carbides R2Ni5C3 (R = La-Nd, Sm, Gd, Tb) are the only representatives of the family of interstitial carbides (i.e., compounds with the composition RxTyCz, where T is a transition metal and 2 ≤ (x + y)/z ≤ 4). The crystal structures (space group P4/mbm) of Sm2Ni5C3 [a = 8.26131(7) Å, c = 3.89090(4) Å, RB = 3.2 %, Rp = 1.3 %] and Gd2Ni5C3 [a = 8.24683(4) Å, c = 3.85398(2) Å, RB = 3.9 %, Rp = 3.6 %] are refined for the first time. They are considered to be built by distorted [R8]-cubes incorporating [CNi6]-octahedra condensed with [C2R8]-trigonal bi-prisms. The structural units are characteristic of the CaTiO3- and AlB2-prototypes, respectively. Temperature dependencies of the magnetic susceptibility, specific heat, electrical resistivity, thermal conductivity, and thermopower in the range 1.8 K (2 K) – 300 K are studied. R2Ni5C3 with R = Nd, Sm, Gd, order antiferromagnetically at TN = 3.4, 6.6, and 22.2 K, respectively. The nature of magnetic transitions in Ce2Ni5C3 at Tmag = 2.3 K and Tb2Ni5C3 at 29.4 K requires further clarification. No magnetic orderings for La2Ni5C3 (Pauli paramagnetic) and Pr2Ni5C3 (Curie-Weiss/van Vleck paramagnetic) are detected. Relatively high electrical resistivities and thermal conductivities, together with the small absolute values of Seebeck coefficients, result in poor thermoelectric performance of the R2Ni5C3 carbides. The calculated electronic structure for La2Ni5C3 indicated a rather low density of states at the Fermi level as well as its extreme sensitivity to any doping. The stabilization of the R2Ni5C3 interstitial carbides up to R = Tb is discussed assuming the rigid-band approach as well as the analysis of selected Ni-C interatomic distances.