Fatto generale: 507 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 507 is the number of rooted ternary trees with 10 vertices.
Trivia: 507 is an uninteresting number.
Data storica: May 21st is the day in 1936 that Sada Abe is arrested after wandering the streets of Tokyo for days with her dead lover's severed genitals in her hand.