1. The problem asks for the best estimate of the sum of $5 \frac{1}{5}$ and $8 \frac{5}{6}$. 2. First, convert the mixed numbers to improper fractions or decimals for easier addition. 3. Convert $5 \frac{1}{5}$: $$5 \frac{1}{5} = 5 + \frac{1}{5} = 5 + 0.2 = 5.2$$ 4. Convert $8 \frac{5}{6}$: $$8 \frac{5}{6} = 8 + \frac{5}{6} \approx 8 + 0.8333 = 8.8333$$ 5. Add the two decimal values: $$5.2 + 8.8333 = 14.0333$$ 6. The sum is approximately $14.03$, which rounds to $14$. 7. Therefore, the best estimate of the sum is $14$.