`5(1)/(7)-{3(3)/(10)-:(2(4)/(5)-(7)/(10))}`

Answer

To solve the expression \( 5\frac{1}{7} - \left\{ 3\frac{3}{10} \div \left( 2\frac{4}{5} - \frac{7}{10} \right) \right\} \), we will follow the order of operations (BODMAS/BIDMAS) which stands for Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- Convert \( 5\frac{1}{7} \):
\[ 5\frac{1}{7} = \frac{5 \times 7 + 1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \]
- Convert \( 3\frac{3}{10} \):
\[ 3\frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{30 + 3}{10} = \frac{33}{10} \]
- Convert \( 2\frac{4}{5} \):
\[ 2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]

2. **Substitute Back into the Expression**:
The expression now looks like:
\[ \frac{36}{7} - \left\{ \frac{33}{10} \div \left( \frac{14}{5} - \frac{7}{10} \right) \right\} \]

3. **Calculate the Expression Inside the Curly Bracket**:
- First, solve \( \frac{14}{5} - \frac{7}{10} \):
- Find a common denominator (which is 10):
\[ \frac{14}{5} = \frac{14 \times 2}{5 \times 2} = \frac{28}{10} \]
- Now subtract:
\[ \frac{28}{10} - \frac{7}{10} = \frac{28 - 7}{10} = \frac{21}{10} \]

4. **Now Divide \( \frac{33}{10} \) by \( \frac{21}{10} \)**:
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{33}{10} \div \frac{21}{10} = \frac{33}{10} \times \frac{10}{21} = \frac{33 \times 10}{10 \times 21} = \frac{33}{21} \]
- Simplifying \( \frac{33}{21} \):
\[ \frac{33 \div 3}{21 \div 3} = \frac{11}{7} \]

5. **Substitute Back into the Expression**:
Now the expression is:
\[ \frac{36}{7} - \frac{11}{7} \]

6. **Perform the Subtraction**:
Since the denominators are the same:
\[ \frac{36 - 11}{7} = \frac{25}{7} \]

### Final Answer:
\[ \frac{25}{7} \]