  This work explores the impact of in-plane bi-axial (epitaxial) strain on the
cation distribution and electric polarization of the Aurivillius-phase compound
Bi$_5$FeTi$_3$O$_{15}$ using first-principles electronic structure
calculations. Our calculations indicate that the site preference of the
Fe$^{3+}$ cation can be controlled via epitaxial strain. Tensile strain
enhances the preference for the inner sites within the perovskite-like layers
of the Aurivillius-phase structure, whereas compressive strain favors
occupation of the outer sites within the perovskite-layers, i.e., the sites
close to the Bi$_2$O$_2$ layer. Controlling the distribution of the magnetic
cations offers the possibility to control magnetic order in this magnetically
dilute system. Furthermore, the magnitude of the electric polarization is
strongly strain-dependent, increasing under tensile strain and decreasing under
compressive strain. Analysis of the Born effective charges reveals strongly
anomalous charges, both of the Bi$^{3+}$ cations and the Ti$^{4+}$ cations.
