let

x = the number of days Paul needs to wash all the windows alone, x>0

y = the number of days John needs to wash all the windows alone, y>0

Paul can wash all the windows on a skyscraper in five days less than john

x = y - 5

working together they can wash all the windows in 6 days this means that in 1 day they will wash

1/x + 1/y = 1/6

by solving the system of equations

x = y - 5

1/x + 1/y = 1/6

we find and consider the positive solutions only (since x>0, y>0)

x = 10 days

y = 15 days

Paul needs 10 days to wash all the windows alone.