I've played many a game, but experiencing a single story at least 5 times must mean it was pretty special. Which story campaigns have you beat at least 5 times? For me I can only think of a few:
MGS 1 - pretty much my favorite game of all time. I think I beat it 8 times on different occasions since 1998.
Resident Evil remake - just about 5 sounds right. I remember trying to get all of the endings.
MGS 4 - this was close, 3 or 4 times trying to beat the game under a certain time.
Your turn, SW.