We report the discovery of five new transiting hot-Jupiter planets discovered by the HATSouth survey, HATS-31b through HATS-35b. These planets orbit moderately bright stars with V magnitudes within the range of - mag while the planets span a range of masses of 0.881.22 MJand have somewhat inflated radii between and . These planets can be classified as typical hot Jupiters, with HATS-31b and HATS-35b being moderately inflated gas giant planets with radii of and 1.64 ±0.22 RJ-1.464+0.069 -0.44, respectively, that can be used to constrain inflation mechanisms. All five systems present a higher Bayesian evidence for a fixed-circular-orbit model than for an eccentric orbit. The orbital periods range from 1.8209993 ±0.0000016 day for HATS-35b) to 3.377960 ± 0.000012 day for HATS-31b. Additionally, HATS-35b orbits a relatively young F star with an age of 2.13 ±0.51Gyr. We discuss the analysis to derive the properties of these systems and compare them in the context of the sample of well-characterized transiting hot Jupiters known to date.