If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.

**Identity.** $\left(x + \dfrac{1}{x}\right)^3 = x^3 + \dfrac{1}{x^3} + 3\left(x + \dfrac{1}{x}\right)$. **Plug in.** $5^3 = x^3 + \dfrac{1}{x^3} + 3 \times 5$, so $125 = x^3 + \dfrac{1}{x^3} + 15 \;\Rightarrow\; x^3 + \dfrac{1}{x^3} = 110$. **Why option D (125) is wrong.** Just cubing the given expression and forgetting the cross-term — the $3xy$ piece must come off, where $xy = 1$ here.