Question 1142283
x is the value of one of the numbers.
y is the value of the other number.


x = y + 5 is one of your equations.
x^2 + y^2 = 193 is the other of your equations.


in the second equation, replace x with y + 5 to get:
(y + 5)^2 + y^2 = 193
simplify to get:
y^2 + 10y + 25 + y^2 = 193
combine like terms to get:
2y^2 + 10y + 25 = 193
subtract 193 from both sides of the equation to get:
2y^2 + 10y - 168 = 0
divide both sides of this equation by 2 to get:
y^2 + 5y - 84 = 0
factor to get:
(y + 12) * (y - 7) = 0
solve for y to get:
y = -12 or y = 7


value of y has to be positive, so y = 7 is a possible solution.
x = y + 5, therefore x = 12
your number appear to be 12 and 7.
12 - 7 = 5, which satisfies one of the requirements.
12^2 + 7^2 = 144 + 49 = 193, which satisfies the other requirement.


your solution is that the numbers are 7 and 12.