Let 'x' and 'y' represent the numbers.

The sum of the numbers is 33:

x + y = 33

The ratio of the numbers is 5/6:

x/y = 5/6 cross-multiply

6x = 5y

We have the following system of equations:

x + y = 33

6x = 5y

........

click here to see the system of equations solved for x and y

........

x = 15

y = 18

The numbers are 15 and 18.