What is a counting number? That is whole digits or integers. no fractions.
List all of the numbers from 1 to 59 (the problem does say "numbers less than 60", which I would assume doesn't include 60.)
1,2,3,4,5, ... 59.
Now how many numbers have at least one 5 in it? 5,15,25...
And don't forget that 50, 51, 52, ... 59 all have the digit "5" in it too.
55 is counted as a number that contains a '5', but don't count the two fives, as the number 55 contains (at least one) 5.
I will leave the counting up to you.
Hope that helps.
+10 
