1. The problem is to solve for $x$ given the equation $x^2 - 4 = 0$ and the condition $x = 5$. 2. The equation to solve is a quadratic equation: $$x^2 - 4 = 0$$ 3. To solve this, we use the zero product property or isolate $x^2$: $$x^2 = 4$$ 4. Taking the square root of both sides, remember to consider both positive and negative roots: $$x = \pm \sqrt{4}$$ $$x = \pm 2$$ 5. The solutions to the equation $x^2 - 4 = 0$ are $x = 2$ and $x = -2$. 6. However, the problem states $x = 5$, which does not satisfy the equation $x^2 - 4 = 0$ because substituting $x=5$ gives: $$5^2 - 4 = 25 - 4 = 21 \neq 0$$ 7. Therefore, $x=5$ is not a solution to the equation $x^2 - 4 = 0$. Final answer: The solutions to $x^2 - 4 = 0$ are $x = 2$ and $x = -2$, but $x=5$ is not a solution.