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 11.9-14.4mag while the planets span a range of masses of 0.88-1.22M_J_ and have somewhat inflated radii between 1.23 and 1.64R_J_. These planets can be classified as typical hot Jupiters, with HATS-31b and HATS-35b being moderately inflated gas giant planets with radii of 1.64+/-0.22R_J_ and 1.464_-0.044_^+0.069^R_J_, 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.