Answer is (-7, -2)
Rewrite the equations so that both are set equal to 0:
y^2 + x^2 = 53
y^2 + x^2 - 53 = 0
y - x = 5
y - x - 5 = 0
Set them equal to eachother:
y^2 + x^2 - 53 = y - x - 5
y^2 + x^2 = y - x + 48
Plug in the value options and see which one works.
A) (-10, -5)
25 + 100 = -5 + 10 + 48 Does not work, eliminate option
B) (-7,-2)
4 + 49 = -2 + 7 + 48
53 = 53 We have a match!
We can stop checking now, we've found the coordinate pair that solves.
Answer is B) (-7, -2)