In general, the difference quotient is [tex]\dfrac{f(x+h)-f(x)}{h}[/tex].
Before we evaluate all of that, we need to find the two top pieces individually.
[tex]\begin{aligned}\\f(x+h) &= -5(x+h)+8 \\[0.5em]&= -5x-5h+8\\\end{aligned}[/tex]
and
[tex]f(x) = -5x+8[/tex]
We'll plug that back into the difference quotient:
[tex]\begin{aligned}\dfrac{f(x+h)-f(x)}{h} &= \dfrac{(-5x-5h+8)-(-5x+8)}{h}\\[0.7em]&= \dfrac{-5x-5h+8+5x-8}{h}\end{aligned}[/tex]
Can you take it from there?
