His Last Bow
Mycroft is seven years older than Sherlock. According to Leslie S. Klinger, Mycroft was born in 1847. A reference in the short story "His Last Bow", which takes place in 1914, suggests that Sherlock is sixty years old at the time the story takes place. This would make the year of Sherlock's birth approximately 1854, and thus Mycroft's approximately 1847.