  The long-period giant planet HR 5183 b has one of the most extreme orbits
among exoplanets known to date, and represents a test for models of their
dynamical evolution. In this work we use Hipparcos-Gaia astrometry to measure
the orbital inclination of this planet for the first time and find
$i=89.9^{+13.3\circ}_{-13.5}$, fully consistent with edge-on. The long orbital
period and high eccentricity of HR 5183 b are supported by our results, with
$P=102^{+84}_{-34}$ years and $e=0.87 \pm 0.04$. We confirm that HR 5183 forms
a physically bound binary with HIP 67291 at a projected separation of 15400 AU,
and derive new constraints on the orbit of this pair. We combine these results
to measure the mutual inclination between the planetary and binary orbits; we
observe significant evidence for misalignment, which remains even after
accounting for bias of the prior towards high mutual inclinations. However, our
results are too imprecise to evaluate a recent prediction that the mutual
inclination should reflect the formation history of HR 5183 b. Further
observations, especially the release of the full Gaia astrometric data, will
allow for improved constraints on the planet-binary mutual inclination. $52 \pm
16\%$ of known planets with eccentricities $e\geq 0.8$ are found in multiple
star systems, a rate that we find to be greater than for the overall planet
population to moderate significance ($p=0.0075$). This supports the hypothesis
that dynamical interactions with wide stellar companions plays an important
role in the formation of highly eccentric exoplanets.
