Abstract We report the discovery by the HATSouth project of five new transiting hot Jupiters (HATS-54b through HATS-58Ab). HATS-54b, HATS-55b, and HATS-58Ab are prototypical short-period ( P  = 2.5–4.2 days, R p  ∼ 1.1–1.2 ) hot Jupiters that span effective temperatures from 1350 to 1750 K, putting them in the proposed region of maximum radius inflation efficiency. The HATS-58 system is composed of two stars, HATS-58A and HATS-58B, which are detected thanks to Gaia DR2 data and which we account for in the joint modeling of the available data—with this, we are led to conclude that the hot Jupiter orbits the brighter HATS-58A star. HATS-57b is a short-period (2.35 day), massive (3.15 ), 1.14 , dense ( ) hot Jupiter orbiting a very active star (2% peak-to-peak flux variability). Finally, HATS-56b is a short-period (4.32 day), highly inflated hot Jupiter (1.7 , 0.6 ), which is an excellent target for future atmospheric follow-up, especially considering the relatively bright nature ( V  = 11.6) of its F dwarf host star. This latter exoplanet has another very interesting feature: the radial velocities show a significant quadratic trend. If we interpret this quadratic trend as arising from the pull of an additional planet in the system, we obtain a period of days for the possible planet HATS-56c, and a minimum mass of . The candidate planet HATS-56c would have a zero-albedo equilibrium temperature of T eq  = 332 ± 50 K, and thus would be orbiting close to the habitable zone of HATS-56. Further radial-velocity follow-up, especially over the next two years, is needed to confirm the nature of HATS-56c.