Mathematical fact: 6427 is the number of ways a 6×6 square can be tiled with 1×1 and 2×2 squares.
Trivia: 6427 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Historical date: August 5th is the day in 1583 that Sir Humphrey Gilbert establishes the first English colony in North America, at what is now St John's, Newfoundland.