Simplify : `10-[8-{9-(8-overline(5-3))}]`.

Answer

To simplify the expression `10 - [8 - {9 - (8 - (5 - 3))}]`, we will follow the order of operations, commonly known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the innermost bracket**: Start with the expression inside the smallest bracket: `(5 - 3)`.
- Calculation:
\[ 5 - 3 = 2 \]
- Now, substitute back into the expression:
\[ 10 - [8 - {9 - (8 - 2)}] \]

2. **Next, solve the expression inside the curly brackets**: Now we have `9 - (8 - 2)`.
- First, calculate `(8 - 2)`:
\[ 8 - 2 = 6 \]
- Substitute back:
\[ 10 - [8 - {9 - 6}] \]

3. **Now, simplify the expression inside the curly brackets**: Calculate `9 - 6`.
- Calculation:
\[ 9 - 6 = 3 \]
- Substitute back:
\[ 10 - [8 - 3] \]

4. **Now, solve the expression inside the square brackets**: Calculate `8 - 3`.
- Calculation:
\[ 8 - 3 = 5 \]
- Substitute back:
\[ 10 - 5 \]

5. **Finally, perform the last subtraction**: Calculate `10 - 5`.
- Calculation:
\[ 10 - 5 = 5 \]

### Final Answer:
The simplified result of the expression `10 - [8 - {9 - (8 - (5 - 3))}]` is **5**.

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