So, what is the case in which he uses the least coins? can he use 1 coin? no, there isn't a 35 cent coin. can he use 2 coins? yes! he can use 25+10 cent coins!
now, the largest number of coins means the coins of the smallest value: so using only 5 cent coins. How many would this be?
we have to divide:
35/5=7
so we would use 7 coins.
And the difference is 5: 7-2 is 5.