If we base it off the day he was found then he's 15. If shin was one or older when he was found then I'm sure merlin would have been able to tell. Even if he was 6 or 9 months when he was found it would still mean he is 15.
Which is too young for our current time and culture. People (or at least girls) used to get married by 13 or younger if they'd hit puberty and were considered getting kind of old for marriage at 15.
B-but they're fifteen