Pressure-composition isotherm measurements show that the ternary lanthanum palladium silicide phase La3Pd5Si absorbs reversibly up to 5 hydrogen atoms per formula unit at 550 K and 14 bar hydrogen pressure. In-situ synchrotron and neutron powder diffraction reveals three phases, an a-phase having the limiting composition La3Pd5SiD similar to 1.6 at low deuterium pressure (at up to 9.5 bar D-2 and 550 K), a beta-phase La3Pd5SiD similar to 2.30-4 at intermediate deuterium pressure (<9.5 bar D-2 and 550 K), and a relatively unstable gamma-phase La3Pd5SiD similar to 5 at high deuterium pressure (obtained at 75 bar D2 and 293 K). While the alpha and beta phases retain the symmetry of the H-free La3Pd5Si (space group Imma), the gamma-phase undergoes a symmetry lowering (a(gamma)similar to a(beta), b(gamma)similar to 3b(beta) and c(gamma)similar to c(beta), V-gamma similar to 3V(beta), space group Pmnb). The structure of the alpha-phase contains isolated [Pd-D-Pd] fragments, which are joined into polymeric (-Pd-D-Pd-)(n) zig-zag chains in the beta-phase. In the gamma-phase some D sites depopulate, while new D sites are occupied, thus leading to a partial interruption of the zig-zag chains and the formation of isolated [D-Pd-D-Pd] and [D-Pd-D-Pd-D) fragments. This unexpected behavior can be attributed to the onset of repulsive Si-D and D-D interactions (Si-D > 3.0 angstrom, D-D > 2.1 angstrom) that divide the structure into Si-poor slabs that absorb hydrogen and Si-rich slabs that do not. The competition between silicon and deuterium which act as a transition metal ligand is further underlined by the fact that Pd atoms having one Si ligand are capable of forming Pd-D bonds, whereas Pd atoms having two Si ligands are not.