1. **State the problem:** We want to determine if $\sqrt{5} < \sqrt{5}^{\sqrt{5}}$ is true. 2. **Rewrite the inequality:** The inequality is $\sqrt{5} < \left(\sqrt{5}\right)^{\sqrt{5}}$. 3. **Recall the properties of exponents:** For any positive number $a > 1$ and exponent $b > 1$, $a < a^b$ holds true. 4. **Evaluate the base and exponent:** Here, $\sqrt{5} \approx 2.236 > 1$ and the exponent $\sqrt{5} \approx 2.236 > 1$. 5. **Apply the rule:** Since both base and exponent are greater than 1, $\sqrt{5} < \left(\sqrt{5}\right)^{\sqrt{5}}$ is true. 6. **Calculate approximate values:** - $\sqrt{5} \approx 2.236$ - $\left(\sqrt{5}\right)^{\sqrt{5}} = 2.236^{2.236} \approx 6.62$ 7. **Conclusion:** $2.236 < 6.62$ confirms the inequality. **Final answer:** $\boxed{\sqrt{5} < \sqrt{5}^{\sqrt{5}}}$ is true.