The given expression is:

$5^3 - (-4)^2 - (-2)^5$

Let's break it down step by step:

Step 1: Evaluate $5^3$

$5^3 = 5 \times 5 \times 5 = 125$

Step 2: Evaluate $(-4)^2$

Since squaring any number makes it positive: $(-4)^2 = (-4) \times (-4) = 16$

Step 3: Evaluate $(-2)^5$

Here, raising a negative number to an odd power gives a negative result: $(-2)^5 = (-2) \times (-2) \times (-2) \times (-2) \times (-2) = -32$

Step 4: Substitute the values back into the original expression:

$125 - 16 - (-32)$

Step 5: Simplify:

$125 - 16 + 32 = 141$

Thus, the result of the expression is 141.

Would you like further details or have any other questions?

Related questions:

1. What happens when a negative number is raised to an even power?
2. How do exponents behave when applied to positive vs negative numbers?
3. What is the difference between even and odd exponents when dealing with negative numbers?
4. Can you explain why the result becomes positive when subtracting a negative number?
5. How does the order of operations affect the result in this expression?

Tip:

When raising negative numbers to powers, remember that even powers make the result positive, while odd powers retain the negative sign.