Answer
$$\lim\limits_{(x,y) \to (1,2)} (5x^3 -x^2y^2) = 1$$
Work Step by Step
Since $5x^3 - x^2y^2$ does not have domain restrictions, we can simply substitute the values for x and y directly into the function:
$\lim\limits_{(x,y) \to (1,2)} (5x^3 -x^2y^2) = 5(1)^3 - (1)^2(2)^2 = 5 - 4 = 1$
