Choice A is the correct answer. Use the algebraic identity.

1. Let: $a = e^x$ and $b = e^{-x}$, so $a + b = 5$.
2. Note: $ab = e^x \cdot e^{-x} = e^0 = 1$.
3. Identity: $(a+b)^2 - (a-b)^2 = 4ab$.
4. Substitute: $25 - (a-b)^2 = 4(1) = 4$.
5. Solve: $(a-b)^2 = 21$, so $a - b = \pm\sqrt{21}$.
6. Wait: Let me verify this using a different method.

Alternatively: $(e^x + e^{-x})^2 = e^{2x} + 2 + e^{-2x} = 25$$e^{2x} + e^{-2x} = 23$

$(e^x - e^{-x})^2 = e^{2x} - 2 + e^{-2x} = 23 - 2 = 21$$e^x - e^{-x} = \pm\sqrt{21}$

So the answer is A, not D!

💡 Strategic Tip:$(a \pm b)^2 = a^2 \pm 2ab + b^2$.