Let's simplify the expression step by step.

Given:

$2 - 5 \left(-3 \left(3 - 5\right) - 2 \left(2 - 3\right)\right)$

Step 1: Simplify the innermost parentheses.

• Inside the first parentheses: $3 - 5 = -2$
• Inside the second parentheses: $2 - 3 = -1$

Now, substitute these values back:

$2 - 5 \left(-3 \left(-2\right) - 2 \left(-1\right)\right)$

Step 2: Multiply inside the parentheses.

• Multiply $-3 \times -2 = 6$
• Multiply $-2 \times -1 = 2$

Substitute these values back:

$2 - 5 \left(6 + 2\right)$

Step 3: Add the values inside the parentheses.

• $6 + 2 = 8$

Now the expression is:

$2 - 5 \times 8$

Step 4: Perform the multiplication.

• $5 \times 8 = 40$

So the expression is now:

$2 - 40$

Step 5: Perform the subtraction.

$2 - 40 = -38$

So, the final simplified value of the expression is:

$\boxed{-38}$

Would you like more details or have any questions?

Here are five related questions for practice:

1. Simplify $4 + 2 \left(5 - 3\left(1 - 4\right)\right)$.
2. Solve $7 - 3 \left(2 \left(4 - 6\right) + 3\left(5 - 2\right)\right)$.
3. Evaluate $6 - 4 \left(-2 \left(3 - 7\right) + 1\right)$.
4. Simplify $3 \times \left(2 - 4 \left(5 - 7\right)\right)$.
5. Solve $8 - 5 \left(-3 \left(4 - 6\right) - 2\right)$.

Tip: Always perform operations inside the parentheses first, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).