Try the Wayback Machine on the Internet Archives:
https://web.archive.org/web/20160304...diaryyear=1940
Not all the little images are captured, but I think all the text is there (a very short section) for Sept 5. I wonder if a full section was never put online.
Re-reading your coment at the start, I think this is exactly what you have. The website may never have put the full day up.
There is another website that has similar information:
https://battle-of-britain-diary.org.uk
Here is the entry for 5 September:
https://battle-of-britain-diary.org.uk/1940/09/05/