Ba5-xLaxNb4-xTixO15 solid solutions were prepared by solid state reaction method. Structural analysis for the stoichiometric phases was performed for x=0, 1, 2 and 3 by Rietveld analysis of neutron powder diffraction data. The x=0, 1 and 2 members could be refined in the space group P-3m1 (stacking sequence chhcc, polytypoid 5 H). There is a decrease in cell volume as x increases. La3+ occupies preferentially the A2 site (Wyckoff site 2d) and Ti4+ the B2 site (Wyckoff site 2c). As x increases there is an increase of the global instability index (GII) (which is a measure of the extent to which the BVS rule is violated over the whole structure) indicating the presence of intrinsic strains large enough to cause instability at room temperature. This strain is responsible for a structural change for the member with x=3, which could be refined in the space group P-3c1 (stacking sequence (chhcc)2, polytypoid 2×5H=10H). This change in space group is associated with a cooperative rotation of (Nb/Ti)O6 octahedra around the c-axis, necessary to accommodate the smaller La3+ ion in the cuboctahedral cavity.