We propose HST/WFC3-IR and ACS observations in 3 bands to characterize the nature and the environment of ADFS-27, the most distant binary hyper-luminous starburst known, at a redshift of 5.655. This rare, gas-rich (Mgas 2.5x10^11Msun), dusty starburst (SFR 2500Msun/yr) system was recently discovered with ALMA and Herschel. It consists of two merging galaxies 2kpc in diameter with dynamical masses of >3x10^11Msun each, separated by only 9kpc, resolved in dust emission by ALMA at 0.15" (1kpc) resolution. We here request imaging of the rest-frame ultraviolet light at matching resolution to measure the unobscured star formation rate, stellar mass and star formation history of this system through a complete SED analysis, as well as the morphology and sizes of the stellar disks and the UV extinction profile. We will also use the multi-band data to search for dropout galaxies in its environment on Mpc scales using the Lyman-break technique, which will put constraints on its formation history and the dark matter halo mass scale. This investigation could reveal the presence of a massive proto-cluster of galaxies within the first billion years of the Big Bang. Finally, the HST imaging will unambiguously address the possibility of a weak gravitational magnification of this system. Given its extreme cosmic rarity, this is key to properly place the existence and evolution of ADFS-27 into context with cosmological simulations and models of starburst galaxies at different epochs. This study will be an important pathfinder for detailed investigations of the most exceptional star-forming environments in the early universe with JWST.