We are given the function $f(x) = 5x - 5$ and we need to evaluate the following expressions:

1. $f(a)$
2. $f(a+h)$
3. $\frac{f(a+h) - f(a)}{h}$

Let's calculate these step by step.

1. $f(a)$

Substitute $a$ into the function $f(x) = 5x - 5$:

$f(a) = 5a - 5$

2. $f(a+h)$

Substitute $a+h$ into the function:

$f(a+h) = 5(a+h) - 5 = 5a + 5h - 5$

3. $\frac{f(a+h) - f(a)}{h}$

Now, subtract $f(a)$ from $f(a+h)$:

$f(a+h) - f(a) = (5a + 5h - 5) - (5a - 5) = 5h$

Finally, divide by $h$:

$\frac{f(a+h) - f(a)}{h} = \frac{5h}{h} = 5$

Final Answers:

1. $f(a) = 5a - 5$
2. $f(a+h) = 5a + 5h - 5$
3. $\frac{f(a+h) - f(a)}{h} = 5$

Would you like more details or have any other questions? Here are five additional related questions:

1. How would the derivative of $f(x) = 5x - 5$ be interpreted geometrically?
2. What happens to the difference quotient as $h \to 0$?
3. How does the constant term $-5$ affect the slope of the function?
4. Can you find the second derivative of $f(x)$?
5. How would this process change if $f(x)$ were a quadratic function?

Tip: The difference quotient $\frac{f(a+h) - f(a)}{h}$ is fundamental in understanding the derivative, which represents the slope of the function at any point.