We report the detection of a 13$\sigma$ H$\alpha$ emission line from HDF850.1 at $z=5.188\pm 0.001$ using the FRESCO (First Reionization Era Spectroscopically Complete Observations) NIRCam F444W grism observations. Detection of H$\alpha$ in HDF850.1 is noteworthy, given its high far-infrared (IR) luminosity, substantial dust obscuration, and the historical challenges in deriving its redshift. HDF850.1 shows a clear detection in the F444W imaging data, distributed between a northern and southern component, mirroring that seen in [C II] from the Plateau de Bure Interferometer. Modelling the spectral energy distribution of each component separately, we find that the northern component has a higher mass, star formation rate (SFR), and dust extinction than the southern component. The observed H$\alpha$ emission appears to arise entirely from the less-obscured southern component and shows a similar $\Delta$v$\sim$ + 130 ${\rm{km\,s}}^{-1}$ velocity offset to that seen for [C II] relative to the source systemic redshift. Leveraging H$\alpha$-derived redshifts from FRESCO observations, we find that HDF850.1 is forming in one of the richest environments identified to date at $z\gt 5$, with 100 $z=5.17$-5.20 galaxies distributed across 13 smaller structures and a $\sim$(15 cMpc)$^3$ volume. Based on the evolution of analogous structures in cosmological simulations, the $z=5.17$-5.20 structures seem likely to collapse into a single $\gt 10^{14}$${\rm M}_{\odot }$ cluster by $z\sim 0$. Comparing galaxy properties forming within this overdensity with those outside, we find the masses, SFRs, and $UV$ luminosities inside the overdensity to be clearly higher. The prominence of H$\alpha$ line emission from HDF850.1 and other known highly obscured $z\gt 5$ galaxies illustrates the potential of NIRCam-grism programs to map both the early build-up of IR-luminous galaxies and overdense structures.