5 6/7 * 5/12 * 1 1/5 : 11/25 = ?

First, convert the mixed numbers to improper fractions:
$$5 \frac{6}{7} = \frac{5 \cdot 7 + 6}{7} = \frac{35 + 6}{7} = \frac{41}{7}$$
$$1 \frac{1}{5} = \frac{1 \cdot 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}$$
Now the expression is:
$$\frac{41}{7} \cdot \frac{5}{12} \cdot \frac{6}{5} : \frac{11}{25}$$
Dividing by a fraction is the same as multiplying by its reciprocal, so we can rewrite the expression as:
$$\frac{41}{7} \cdot \frac{5}{12} \cdot \frac{6}{5} \cdot \frac{25}{11}$$
Now, multiply the fractions:
$$\frac{41 \cdot 5 \cdot 6 \cdot 25}{7 \cdot 12 \cdot 5 \cdot 11} = \frac{41 \cdot 5 \cdot 6 \cdot 5 \cdot 5}{7 \cdot 6 \cdot 2 \cdot 5 \cdot 11} = \frac{41 \cdot 5 \cdot 5}{7 \cdot 2 \cdot 11} = \frac{41 \cdot 25}{14 \cdot 11} = \frac{1025}{154}$$
Now convert the improper fraction to a mixed number:
$$\frac{1025}{154} = 6 \frac{1025 - 6 \cdot 154}{154} = 6 \frac{1025 - 924}{154} = 6 \frac{101}{154}$$

Answer: 6 101/154