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To solve this problem, we need to find the **average rate of change** of the function \( g(x) = 5x^2 + 5 \) over the interval \([x, x+h]\).

### Steps:
The average rate of change of a function \(g(x)\) over an interval \([a, b]\) is given by:

\[
\text{Average rate of change} = \frac{g(b) - g(a)}{b - a}
\]

Here, the interval is \([x, x+h]\), so:

- \(a = x\)
- \(b = x + h\)

Now, apply the formula:

1. **Calculate \(g(x)\)**:
   \[
   g(x) = 5x^2 + 5
   \]

2. **Calculate \(g(x+h)\)** (substitute \(x+h\) into the function):
   \[
   g(x+h) = 5(x+h)^2 + 5 = 5(x^2 + 2xh + h^2) + 5 = 5x^2 + 10xh + 5h^2 + 5
   \]

3. **Subtract \(g(x)\) from \(g(x+h)\)**:
   \[
   g(x+h) - g(x) = (5x^2 + 10xh + 5h^2 + 5) - (5x^2 + 5) = 10xh + 5h^2
   \]

4. **Divide by the difference in the interval \(h\)**:
   \[
   \text{Average rate of change} = \frac{10xh + 5h^2}{h}
   \]

5. **Simplify**:
   \[
   \frac{10xh + 5h^2}{h} = 10x + 5h
   \]

### Final Answer:
The average rate of change of \(g(x)\) over the interval \([x, x+h]\) is:

\[
10x + 5h
\]

Let me know if you need further details or explanations! 

Here are 5 related questions you might explore:
1. What is the geometric interpretation of the average rate of change of a function?
2. How does the average rate of change relate to the derivative of a function?
3. How would the average rate of change change if the function was \(g(x) = ax^2 + bx + c\)?
4. Can the average rate of change ever be zero? If so, under what conditions?
5. How does the average rate of change differ from instantaneous rate of change?

**Tip:** For quadratic functions, the average rate of change depends on both the starting point and the length of the interval, unlike linear functions.

Find the average rate of change of the function g(x) = 5x^2 + 5 on the interval [x, x+h].

This problem demonstrates how to find the average rate of change of the quadratic function g(x) = 5x^2 + 5 over the interval [x, x+h]. Using key algebraic concepts and formulas, students in Grades 10-12 can learn the process step-by-step.

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