Binary and pseudo-binary compounds Ln 5 Si 3 - x M x (Ln=La, Ce or Nd; M=Ni or Co) were prepared by arc-melting the constituent elements under high purity argon on a water-cooled copper hearth and their structures were refined from single X-ray data. The binary La 5 Si 3 and various ternary compounds were synthesized: La 5 Ni 0 . 1 2 9 Si 2 . 8 7 1 , La 5 Ni 0 . 2 6 5 Si 2 . 7 3 5 , Ce 5 Ni 0 . 3 5 5 Si 2 . 6 4 5 , Nd 5 Ni 0 . 6 3 3 Si 2 . 3 6 7 , La 5 Co 0 . 3 Si 2 . 7 and Nd 5 Co 0 . 3 1 Si 2 . 6 9 . All these compounds crystallize with the Cr 5 B 3 structure type (tetragonal, space group I4/mcm). The refinement shows a mixed occupancy on a particular site between Si and the M element. Therefore, a non-harmonic displacement of the rare-earth close to this site has been observed. Ab initio band structure calculations have been performed to address the electronic structure of these compounds and to explain the non-harmonic displacement of the rare-earth atoms in the structure.