[en] Two Hubble Space Telescope narrow-band Hα images separated in time by 1.03 years are used for a proper motion measurement of the forward shock of the LMC supernova remnant 0509–67.5, the only spectroscopically confirmed LMC remnant of Ia origin. We measure a global shock speed of 6500 ± 200 km s⁻¹ and constrain the pre-shock neutral hydrogen density to be 0.084 ± 0.003 cm⁻³, for a typical mean number of Hα photons produced per neutral hydrogen atom entering the forward shock. Previously published broad Hα line widths from two locations on the rim and our corresponding shock speed measurements are consistent with Balmer shock models that do not include effects of cosmic-ray acceleration. For the northeastern rim location, we limit the post-shock electron temperature to 10% of the proton temperature by also using the broad-to-narrow flux ratio. Hydrodynamic simulations for different initial ejecta density profiles constrain the age and ambient medium density; for an exponential ejecta profile and initial explosion energy of 1.4 × 10⁵¹ erg, the remnant’s age is ${310}_{-<!--\; ???\; -->30}^{+40}$ years. For all evolutionary models explored, the expansion parameter falls in the range of 0.41–0.73, indicating that the remnant is still firmly in the ejecta-dominated phase of its evolution. Our measured neutral hydrogen density of the ambient medium, combined with the shocked density obtained in Williams et al., disfavors forward shock compression factors greater than ∼7.