  We present new XMM-Newton and NuSTAR observations of the galaxy merger IRAS
F05189-2524 which is classified as an ultra-luminous infrared galaxy (ULIRG)
and optical Seyfert 2 at $z$ = 0.0426. We test a variety of spectral models
which yields a best-fit consisting of an absorbed power law with emission and
absorption features in the Fe K band. Remarkably, we find evidence for a
blueshifted Fe K absorption feature at $E$ = 7.8 keV (rest-frame) which implies
an ultra-fast outflow (UFO) with $v_{\mathrm{out}} = 0.11\ \pm\ 0.01c$. We
calculate that the UFO in IRAS F05189-2524 has a mass outflow rate of
$\dot{M}_{\mathrm{out}}\ \gtrsim 1.0\ M_\odot$ yr$^{-1}$, a kinetic power of
$\dot{E}_{\mathrm{K}} \gtrsim$ 8% $L_{\mathrm{AGN}}$, and a momentum rate (or
force) of $\dot{P}_{\mathrm{out}}\ \gtrsim 1.4\ L_{\mathrm{AGN}}/c$. Comparing
the energetics of the UFO to the observed multi-phase outflows at kiloparsec
scales yields an efficiency factor of $f\sim0.05$ for an energy-driven outflow.
Given the uncertainties, however, we cannot exclude the possibility of a
momentum-driven outflow. Comparing IRAS F05189-2524 with nine other objects
with observed UFOs and large-scale galactic outflows suggests that there is a
range of efficiency factors for the coupling of the energetics of the nuclear
and galaxy-scale outflows that likely depend on specific physical conditions in
each object.
