The expression given is:
$\left(-2^5\right)$

Step 1: Understanding the Order of Operations

According to the order of operations (PEMDAS/BODMAS rules):

1. Exponentiation is performed before applying the negative sign unless parentheses dictate otherwise.
2. The given expression can be interpreted as:
   $-(2^5)$

Step 2: Compute the Exponentiation

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

Step 3: Apply the Negative Sign

$-(2^5) = -32$

Final Answer:

$\mathbf{-32}$

Would you like a more detailed explanation? Let me know if you have any questions!

Related Questions:

1. How does the placement of parentheses change exponentiation in negative numbers?
2. What is the difference between $(-2)^5$ and $-2^5$?
3. How do exponents affect the sign of a number?
4. What is the general rule for exponentiation of negative numbers?
5. How does the order of operations influence mathematical expressions?

Math Tip:

Always be cautious with negative numbers and exponents—parentheses change the meaning significantly!