In this sort of situation, parents often turn up with a copy of an announcement in the newspaper (it helps, of course, if the surname matches), or death certificate.
The best evidence would have been confirmation from school that DS was not his usual self during the fortnight in question, or signs in exercise books that work was not up to his usual standard.
Failing that, and assuming things weren't so serious that a GP or counsellor became involved, I'm afraid it's very difficult to establish the effect on the child.
I think many panels would give a bit of weight to the disruption, although it's far from clear how much his reasoning ability would have improved as a result of practice in the two weeks before the test. If the gap were just a mark or two, I'd be more confident.
By all means mention the extenuating circumstances, but my advice would be not to overdo them. Academic evidence is usually the key. Three 5s are all right as a starting point. G&T is encouraging, although it's not a fixed standard as it depends entirely on the standard within the school.
Appeals can be very unpredictable, so - if you can put up with all the stress - it's worth seeing what a panel thinks of your case as a whole.