Greyback attacks Remus in revenge for Lyall‘s unguarded comments that werewolves are “soulless, evil, deserving nothing but death.” Shortly before Remus’s fifth birthday, the tenth of March, Greyback breaks into Remus’s bedroom and bites him. Lyall arrives in time to drive Greyback away, but the damage was done.
Assuming that Greyback attacked Remus during a full moon, we can use the real world calendar to determine the probable dates. Again making an assumption, we will say that the attack happened very close to Remus' fifth birthday, from which we can determine that either February 16th or January 17th qualify. We're going to go with the February date as the most likely.