1. **Simplify:** $\ln\left(\frac{1}{2}\right) + \ln\left(\frac{2}{3}\right) + \ln(5)$ 2. Use the logarithm property: $\ln(a) + \ln(b) = \ln(ab)$. 3. Combine the first two terms: $$\ln\left(\frac{1}{2}\right) + \ln\left(\frac{2}{3}\right) = \ln\left(\frac{1}{2} \times \frac{2}{3}\right) = \ln\left(\frac{\cancel{1} \times \cancel{2}}{\cancel{2} \times 3}\right) = \ln\left(\frac{1}{3}\right)$$ 4. Now add $\ln(5)$: $$\ln\left(\frac{1}{3}\right) + \ln(5) = \ln\left(\frac{1}{3} \times 5\right) = \ln\left(\frac{5}{3}\right)$$ **Final answer:** $\ln\left(\frac{5}{3}\right)$