The fifth symphony was a piece of music composed by Ludwig van Beethoven.
The Twelfth Doctor used it to illustrate the "bootstrap paradox", referring to a time traveller who went back in time to meet his hero Beethoven, only to find that he did not exist, prompting him to use his future knowledge to produce the works attributed to Beethoven himself, meaning that the traveller was inspired by himself, and therefore all knowledge and events were self perpetuating and paradoxical. Posing the question "Who wrote Beethoven's fifth?", he took out an electric guitar and played the symphony's opening bars. (TV: Before the Flood)
Later, when he was a lecturer at St Luke's University for over fifty years, the same Doctor began to play the symphony on his electric guitar when Bill Potts arrived in his office. (TV: The Pilot)
The Tenth Doctor once said that "Beethoven's Fifth" could be rhyming slang for "Mickey Smith". (PROSE: Legends of Camelot)