let 'x' and 'y' represent the numbers and x>y

The difference between two numbers is five:

x - y = 5

x = 5 + y

The sum of the squares of the numbers is 157:

x^2 + y^2 = 157

plug x = 5 +y into the last equation:

(5 + y)^2 + y^2 = 157

by solving we find:

y = 6

click here to see the step by step solution of the equation:

x = 5 + 6

x = 11

the numbers are 11 and 6.