1. **State the problem:** We are given five numbers: 5, 9, x, 17, and 21. Their mean (average) is 13. We need to find the value of $x$. 2. **Formula for mean:** The mean of $n$ numbers $a_1, a_2, ..., a_n$ is given by $$\text{Mean} = \frac{a_1 + a_2 + \cdots + a_n}{n}$$ 3. **Apply the formula:** Here, $n=5$ and the mean is 13, so $$13 = \frac{5 + 9 + x + 17 + 21}{5}$$ 4. **Simplify the numerator:** $$5 + 9 + 17 + 21 = 52$$ 5. **Rewrite the equation:** $$13 = \frac{52 + x}{5}$$ 6. **Multiply both sides by 5 to clear the denominator:** $$13 \times 5 = 52 + x$$ $$65 = 52 + x$$ 7. **Solve for $x$:** $$x = 65 - 52$$ $$x = 13$$ **Final answer:** The value of $x$ is 13.