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 $fsim0.05$ 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.
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