It is 15 minutes late, that is, if it is half past nine, then it is actually nine and 45 minutes
5 minutes advanced means that if it is half past nine, it is actually nine and 25 minutes (for our friend)
So the hour will actually be nine and 45 minutes, regardless of what he thinks, since you decided that the truth is that it is a quarter of an hour late.
But the question is, will he say the clock as it is or will he reduce the five minutes that he thinks his watch is ahead of
If he were to say what in the hour without any decrease, the correct timing would be 9:45 minutes
If it will decrease the five minutes, then the correct timing will be nine and 50 minutes because it will delay it in addition to the quarter an hour, five more minutes, i.e. twenty minutes