Fait mathématique: 5679 is the number of drawings of the complete graph K_{10} with a minimal number of crossings.
Culture générale: 5679 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Date historique: July 19th is the day in 1961 that Tunisia imposes a blockade on the French naval base at Bizerte; the French would capture the entire town four days later.