I didn't look at the question in the exam, what kind of sadist begins a question with "Write down the character table of D10"?
That said, I think we can see it's A5 since it has 24 elements of order 5 and therefore 6 5-sylow subgroups. I seem to remember this implies that this was enough to show it's A5. (But obviously I wouldn't have touched this question with a barge-pole).