Age is nothing but a number, as long as she's not under age. A lot of younger girls are really mature this days but parents don't see that cuz they want someone that all ready has an education set, and a good job. good luck man don't let this affect your relationship with your girl, explain to your parents how she is and how that makes you feel maybe it helps..
It's only a 5 year difference, so it's really not that much. My parents are 9 years apart. Hell, my dad met my mom when he was 26 and she was 17.
You have nothing to worry about. :)
Btw, you're 24, you don't need your fams approval.