1. **State the problem:** Factor the quadratic expression $5x^2 - 80$. 2. **Formula and rules:** To factor expressions, first look for the greatest common factor (GCF). Then factor it out. 3. **Find the GCF:** The GCF of $5x^2$ and $-80$ is 5. 4. **Factor out the GCF:** $$5x^2 - 80 = 5(x^2 - 16)$$ 5. **Recognize difference of squares:** $x^2 - 16$ is a difference of squares since $16 = 4^2$. 6. **Apply difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ 7. **Factor $x^2 - 16$:** $$x^2 - 16 = (x - 4)(x + 4)$$ 8. **Write the fully factored form:** $$5x^2 - 80 = 5(x - 4)(x + 4)$$ **Final answer:** $5(x - 4)(x + 4)$