1. **State the problem:** Simplify the expression $$\frac{1}{\sqrt{5} - 2} \times \frac{1}{\sqrt{5} + 2}$$. 2. **Recall the formula:** When multiplying expressions with conjugates in the denominator, use the difference of squares formula: $$ (a - b)(a + b) = a^2 - b^2 $$. 3. **Multiply the two fractions:** $$\frac{1}{\sqrt{5} - 2} \times \frac{1}{\sqrt{5} + 2} = \frac{1 \times 1}{(\sqrt{5} - 2)(\sqrt{5} + 2)}$$ 4. **Apply the difference of squares:** $$= \frac{1}{(\sqrt{5})^2 - (2)^2} = \frac{1}{5 - 4}$$ 5. **Simplify the denominator:** $$= \frac{1}{1}$$ 6. **Final answer:** $$1$$ The expression simplifies to 1.