I suspect even moderate sleep deprivation or a mild headache can (temporarily) impair your cognitive abilities by more than 5 IQ points.

I suspect you are right and if I recall correctly the sleep deprivation -> IQ loss relationship has even been quantized!

When I was in highschool, I tried to do physics 'olympiads'. The issue was, they were 2 hours from where I lived, and started 9am, and were marathon style (five frigging hours for 5..10 hard problems). So that's waking up 6:30, quickly having breakfast, then public transportation for 2 hours being wobbled around in train, subway, bus, and another train. I didn't do too great on those even though I did ace harder problems normally (e.g. in school). I think eating chocolate to make yourself more awake or drinking strong tea also did not work for me at all; later when I started working in software development I had enough time to see that this only impairs my performance further.