1. **State the problem:** Simplify the expression $\frac{1}{5} \ln 32 - \ln 2$. 2. **Recall logarithm rules:** - $a \ln b = \ln b^a$ - $\ln a - \ln b = \ln \frac{a}{b}$ 3. **Apply the power rule:** $$\frac{1}{5} \ln 32 = \ln 32^{\frac{1}{5}}$$ 4. **Calculate $32^{\frac{1}{5}}$:** Since $32 = 2^5$, $$32^{\frac{1}{5}} = (2^5)^{\frac{1}{5}} = 2^{5 \times \frac{1}{5}} = 2^1 = 2$$ 5. **Rewrite the expression:** $$\ln 2 - \ln 2$$ 6. **Use the subtraction rule:** $$\ln \frac{2}{2} = \ln 1$$ 7. **Evaluate $\ln 1$:** $$\ln 1 = 0$$ **Final answer:** $0$