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The problem provided asks to subtract two expressions:

\[
(5x^2 + 8) - (7x^2 - 5)
\]

Let's simplify this step by step.

### Step 1: Distribute the negative sign
When subtracting, you distribute the negative sign to each term inside the parentheses:

\[
(5x^2 + 8) - (7x^2 - 5) = 5x^2 + 8 - 7x^2 + 5
\]

### Step 2: Combine like terms
Now, combine the \(x^2\) terms and the constants:
- \(5x^2 - 7x^2 = -2x^2\)
- \(8 + 5 = 13\)

### Final result:
\[
-2x^2 + 13
\]

So, the simplified expression is:

\[
(5x^2 + 8) - (7x^2 - 5) = -2x^2 + 13
\]

Let me know if you need further clarification or any additional details.

Here are 5 related questions to expand on this:
1. How do you distribute a negative sign across an expression?
2. Can you add or subtract terms with different powers of \(x\)?
3. What happens if both expressions have more variables?
4. How do you handle similar subtraction problems with cubic terms, like \(x^3\)?
5. What is the importance of like terms when simplifying expressions?

**Tip**: Always be careful with the signs when subtracting or distributing! Misplacing a negative can change the whole expression.

Learn how to subtract two polynomials: (5x^2 + 8) - (7x^2 - 5). This problem covers key algebraic concepts such as distributing negative signs and combining like terms. Suitable for students in Grades 8-10.

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