first the 5 and 10 minute people cross, then the 5 minute person goes back with lantern ( so 15minutes is used ) and you have 5,20 and 25 still to cross
then the 20 and 25 minute goes across ( which means 25 +15 = 40mins is used )
then 10mintue person ( which has already crossed ) , goes back to the start with the lantern ( which means 40+10 =50mintues used ).
then the 5 and 10mintue cross ( 10+50 =60mintues ) and all have crossed .