1. **State the problem:** Evaluate $\log_5 \left(5^{3\sqrt{5}}\right)$. 2. **Recall the logarithm power rule:** For any base $a > 0$, $a \neq 1$, and any exponent $x$, $\log_a \left(a^x\right) = x$. 3. **Apply the rule:** Here, the base of the logarithm and the base of the exponent are both 5, so $$\log_5 \left(5^{3\sqrt{5}}\right) = 3\sqrt{5}.$$ 4. **Final answer:** $$\boxed{3\sqrt{5}}$$