1. Stating the problem: We are given two points, P(-2, -2) and Q(x, 2), and the length of the line segment PQ is 5 units. 2. Use the distance formula between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Here, $d = 5$, $x_1 = -2$, $y_1 = -2$, $x_2 = x$, and $y_2 = 2$. 3. Substitute the known values into the formula: $$5 = \sqrt{(x - (-2))^2 + (2 - (-2))^2}$$ This simplifies to: $$5 = \sqrt{(x + 2)^2 + (4)^2}$$ 4. Square both sides to eliminate the square root: $$25 = (x + 2)^2 + 16$$ 5. Subtract 16 from both sides: $$25 - 16 = (x + 2)^2$$ $$9 = (x + 2)^2$$ 6. Take the square root of both sides: $$x + 2 = \pm 3$$ 7. Solve for $x$: - If $x + 2 = 3$, then $x = 1$. - If $x + 2 = -3$, then $x = -5$. 8. The problem asks for the positive value of $x$, so the answer is: $$\boxed{1}$$