Why do some people say that 'Beethoven's Fifth' actually came after his sixth symphony?

Portrait of Beethoven

When Beethoven's Fifth and Sixth Symphonies premiered 201 years ago today — on December 22, 1808 — the Sixth was played before the Fifth, even though the Fifth was actually written a bit before the other. The two pieces premiered at Vienna's Theater an der Wien, with Ludwig van Beethoven himself conducting. The concert lasted four hours and included other Beethoven premiers, as well; The Choral Fantasy and his Fourth Piano Concerto were among the pieces played. Beethoven played the piano concerto — his last time appearing as a soloist with the orchestra.

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