The long-period giant planet HR 5183 b has one of the most extreme orbits among exoplanets known to date. In this work we use Hipparcos-Gaia astrometry to measure the orbital inclination of this planet for the first time. We measure 𝑖 = 89.9 +13.3• −13.5 , fully consistent with an edge-on orbit. The previously reported 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 ± 0.04. We confirm that HIP 67291 forms a physically bound binary with HR 5183 at a projected separation of 15400 AU, and derive new constraints on the orbit of this pair. We combine our inclination measurements in an attempt to measure the mutual inclination between the planetary and binary orbits; while there is some evidence for misalignment, we conclude that this is not statistically significant. Further observations, especially the release of the full Gaia astrometric data, will allow for improved constraints on the planet-binary mutual inclination in this system. 52 ± 16% of known planets with eccentricities 𝑒 ≥ 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.