1. **Problem:** Given $a = \sqrt{5 + 2}$ and $b = \sqrt{5 - 2}$, find $a^2 - b^2$. 2. **Formula and rules:** Recall the difference of squares formula: $a^2 - b^2 = (a - b)(a + b)$. Also, squaring a square root cancels the root: $(\sqrt{x})^2 = x$. 3. **Calculate $a^2$ and $b^2$:** $$a^2 = 5 + 2 = 7$$ $$b^2 = 5 - 2 = 3$$ 4. **Find $a^2 - b^2$:** $$a^2 - b^2 = 7 - 3 = 4$$ 5. **Answer:** $$\boxed{4}$$