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Small inner companions to giant planets with $P \\lesssim$ 15 days are known only in five compact systems: WASP-47, Kepler-730, WASP-132, TOI-1130, and TOI-2000. Here, we report the confirmation of TOI-5398, the youngest compact multi-planet system composed of a hot sub-Neptune (TOI-5398 c, $P_{\\rm c}$ = 4.77271 days) orbiting interior to a short-period Saturn (TOI-5398 b, $P_{\\rm b}$ = 10.590547 days) planet, both transiting around a 650 $\\pm$ 150 Myr G-type star. As part of the GAPS Young O","authors_text":"A. Anna John, A. Bieryla, A. Bignamini, A. Bonomo, A. C. Cameron, A. F. Lanza, A. Fukui, A. Ghedina, A. Maggio, A. Shporer, A. Sozzetti, A. Vanderburg, C. Watkins, D. Cheryasov, D. Gandolfi, D. Locci, D. Nardiello, D. Polychroni, D. Turrini, D. W. Latham, E. Pall\\'e, F. Borsa, F. Murgas, G. Fur\\'esz, G. Mantovan, G. Nowak, G. Piotto, G. Scandariato, H. Boffin, H. Parviainen, H. Relles, I. Strakhov, J. Dong, J. D. Twicken, J. Jenkins, J. J. Lissauer, J. Maldonado, J. N. Winn, J. Orell-Miquel, K. A. Collins, K. Barkaoui, K. Biazzo, K. McLeod, K. Stassun, L. Borsato, L. Cabona, L. Malavolta, M. Baratella, M. Damasso, M. D'Arpa, M. Endl, M. Molinaro, M. Montalto, M. Pedani, N. Narita, P. Benni, P. Kab\\'ath, P. Rowden, R. Claudi, R. Luque, R. Schwarz, S. Benatti, S. Desidera, S. Messina, S. N. Quinn, S. Seager, T. G. Wilson, T. Zingales, V. Lorenzi, V. Nascimbeni, W. Cochran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.EP","submitted_at":"2023-10-25T18:00:02Z","title":"The GAPS programme at TNG XLIX. 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