Let's simplify the expression step by step:

The given expression is:

\[
5\{−1+4[1−3(−5+4)]\}
\]

### Step 1: Simplify inside the innermost parentheses.
The innermost part is \( -5 + 4 \):

\[
-5 + 4 = -1
\]

Now, the expression becomes:

\[
5\{−1+4[1−3(−1)]\}
\]

### Step 2: Simplify inside the brackets.
Now, handle the multiplication within the square brackets. First, multiply \( -3 \) by \( -1 \):

\[
-3 \times (-1) = 3
\]

Now, the expression becomes:

\[
5\{−1+4[1+3]\}
\]

### Step 3: Add inside the square brackets.
Add \( 1 + 3 \) to get:

\[
1 + 3 = 4
\]

Now the expression is:

\[
5\{−1+4(4)\}
\]

### Step 4: Multiply inside the braces.
Multiply \( 4 \times 4 \) to get:

\[
4 \times 4 = 16
\]

Now the expression is:

\[
5\{−1+16\}
\]

### Step 5: Simplify inside the braces.
Add \( -1 + 16 \):

\[
-1 + 16 = 15
\]

Now the expression is:

\[
5(15)
\]

### Step 6: Final multiplication.
Multiply \( 5 \times 15 \):

\[
5 \times 15 = 75
\]

### Final Answer:
The value of the expression is:

\[
\boxed{75}
\]

Would you like further details, or do you have any questions?

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Here are five related questions:
1. What is the order of operations (PEMDAS/BODMAS)?
2. How do parentheses impact mathematical operations?
3. How do negative signs affect multiplication and addition?
4. How can distributing numbers help simplify expressions?
5. How do you deal with nested parentheses?

**Tip:** Always handle operations inside parentheses or brackets first before moving to outer operations.

Learn how to simplify the expression 5{−1+4[1−3(−5+4)]} step-by-step by following the order of operations. This solution covers handling nested parentheses, multiplication, and addition, making it suitable for students in Grades 6-8.

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