Answer:

6 and 11

Step-by-step explanation:

let x  = one number

   y = other number

x - y = 5 .        ========= x = y + 5

x^2 + y^2 = 157

Substitute  y + 5 to x  

    (y +5)^2 + y^2 = 157

   y^2 + 10y + 25 + y^2 = 157

  2y^2 + 10y +25 - 157 = 0

  2y^2 + 10y  - 132 = 0

  2 ( y^2 + 5y - 66 ) = 0

  2 ( y +11 ) ( y - 6) = 0

      y = -11 ;  y = 6  

    y = 6  ( one number)

    x - 6 = 5

    x = 6 + 5  = 11 ( the other number)