Evaluate:
`7-[3-5(4+7)+4{14 div (35 div 5)}]`

Answer

To evaluate the expression \( 7 - [3 - 5(4 + 7) + 4 \{ 14 \div (35 \div 5) \}] \), we will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

### Step-by-Step Solution:

1. **Evaluate the innermost expression**: Start with \( 35 \div 5 \).
\[ 35 \div 5 = 7 \]
Now substitute this back into the expression:
\[ 7 - [3 - 5(4 + 7) + 4 \{ 14 \div 7 \}] \]

2. **Evaluate \( 14 \div 7 \)**:
\[ 14 \div 7 = 2 \]
Substitute this back:
\[ 7 - [3 - 5(4 + 7) + 4 \times 2] \]

3. **Calculate \( 4 + 7 \)**:
\[ 4 + 7 = 11 \]
Substitute this back:
\[ 7 - [3 - 5 \times 11 + 4 \times 2] \]

4. **Calculate \( 5 \times 11 \)**:
\[ 5 \times 11 = 55 \]
Substitute this back:
\[ 7 - [3 - 55 + 4 \times 2] \]

5. **Calculate \( 4 \times 2 \)**:
\[ 4 \times 2 = 8 \]
Substitute this back:
\[ 7 - [3 - 55 + 8] \]

6. **Combine the terms inside the brackets**:
\[ 3 - 55 + 8 = 3 - 55 = -52 \quad \text{then} \quad -52 + 8 = -44 \]
Substitute this back:
\[ 7 - [-44] \]

7. **Subtracting a negative**:
\[ 7 - (-44) = 7 + 44 = 51 \]

### Final Answer:
\[ \boxed{51} \]