Just to corroborate what Charles wrote, here's the entry from Britannica:
https://www.britannica.com/topic/Symphony-No-5-in-C-Minor-Op...I quote:
"Beethoven himself allegedly described the figure as 'fate knocking at the door.' It is an evocative image, but the source of the attribution, Beethoven’s sometime friend Anton Schindler, was known for not letting facts get in the way of a good story."
The author is from the States. Perhaps that's why she goes on to say:
"In any event, the notion of the 'fate' theme, or 'fate' motif, has remained a popular one."
However, not once does the author use the word "fate" to describe the entire piece. Neither does Tom Service, a music journalist who has written about classical music for the Guardian since 1999:
https://www.theguardian.com/music/tomserviceblog/2013/sep/16...Best