i) births and deaths

5 September 1964: birth of Stephen Greenhorn, writer of The Lazarus Experiment (2007) and The Doctor's Daughter (2008).

5 September 1987: death of Bill Fraser, who played General Grugger in Meglos (Fourth Doctor, 1980) and Bill Pollock in K9 and Company.

ii) broadcast anniversary

5 September 1964: broadcast of "A Bargain of Necessity", fifth episode of the story we now call The Reign of Terror. Ian is rescued; the Doctor attempts to rescue Susan; but is forced to  cooperate with Lemaitre instead. A lost episode, sadly, but it has been animated.

iii) date specified in-universe:

5 September 2954: birth of Chris Cwej, one of the Seventh Doctor’s companions in the New Adventures.