A quarter hour (15 minutes) before 5:55 is gotten by subtracting:

       5:55
      - :45
      ————— 
       5:10

So he must be home by 5:10 so we subtract 32 minutes from 5:10:

       5:10
      - :32
      —————

But we must borrow 1 hour, which is 60 minutes, from the 5 hours,
making it 4 hours.  Then we add 60 minutes onto the minutes, so
we replace the 5:10 by 4:70, so we can subtract a smaller number
for a 

       4:70
      - :32
      —————
       4:38  So he must leave by 4:38

Edwin

A quarter of an hour before  5:55  is  5:40.


32 minutes before 5:40 is 5:08.


It is the latest time Max must leave to be home by a quarter before 5:55.