  We report the structural and magnetic properties of four-layer Aurivillius
compound Bi$_5$FeTi$_3$O$_{15}$ (BFTO) at high hydrostatic pressure conditions.
The high-pressure XRD data does not explicitly show structural phase
transitions with hydrostatic pressure, however the observed changes in lattice
parameters indicate structural modifications at different pressure values. In
the initial pressure region values, the lattice parameters $\textit{a}$- and
$\textit{b}$- are nearly equal implying a quasi-tetragonal structure, however
as the pressure increases $\textit{a}$- and $\textit{b}$- diverges apart and
exhibits complete orthorhombic phase at pressure values of about $\geq$8 GPa.
Principal component analysis of high pressure Raman measurements point out an
evident change in the local structure at about 5.5 GPa indicating that the
evolution of the local structure under applied pressure seems to not follow
crystallographic changes (long range order). Nuclear forward scattering (NFS)
measurement reveal the development of magnetic ordering in BFTO at 5K with high
pressures. A progressive increase in magnetic order is observed with increase
in pressure at 5K. Further, NFS measurements carried out at constant pressure
(6.4GPa) and different temperatures indicate that the developed magnetism
disappears at higher temperatures (20K). It is attempted to explain these
observations in terms of the observed structural parameter variation with
pressure.
