5 June 1908: birth of Bill Fraser, who played General Grugger in Meglos (Fourth Doctor, 1980) and Bill Pollock in K9 and Company.
5 June 1917: birth of Anne Tirard, who played Locusta the poisoner in the story we now call The Romans (First Doctor, 1965) and the Seeker in The Ribos Operation (Fourth Doctor, 1978).
5 June 1919: birth of Laurence Payne, who played Johnny Ringo in the story we now call The Gunfighters (First Doctor, 1966), Morix in The Leisure Hive (Fourth Doctor, 1980), and Dastari in The Two Doctors (Sixth and Second Doctors, 1985).
5 June 1925: birth of Bill Sellars, who directed The Celestial Toymaker (First Doctor, 1966).
5 June 2012: death of Caroline John, who played Liz Shaw, the Third Doctor's companion in 1970.
ii) broadcast anniversaries
5 June 1966: broadcast of "Flight Through Eternity", third episode of the story we now call The Chase. First appearance of Peter Purves, though not as Steven Taylor. The Tardis, pursued by the Daleks, lands on the Empire State Building and the Mary Celeste.
5 June 1971: broadcast of third episode of The Dæmons. The Doctor and the Brigadier try to penetrate the heat shield around the village.
5 June 2010: broadcast of Vincent and the Doctor. The Doctor investigates a mysterious creature in one of van Gogh's paintings and gets entangled with the Krafayis.
iii) date specified in canon
5 June 1994: birth of Clyde Langer (as in the Sarah Jane Adventures).