this looks suspiciously like the difference quotient
anyway
evaluate each then put them together
[tex]f(a+h)=(a+h)^2-5(a+h)[/tex]
[tex]f(a+h)=a^2+2ah+h^2-5a-5h[/tex]
[tex]f(a+h)=a^2+2ah-5a-5h+h^2[/tex]
[tex]f(a)=a^2-5a[/tex]
so [tex]\frac{f(a+h)-f(a)}{h}=[/tex]
[tex]\frac{a^2+2ah-5a-5h+h^2-(a^2-5a)}{h}=[/tex]
[tex]\frac{a^2+2ah-5a-5h+h^2-a^2+5a}{h}=[/tex]
[tex]\frac{2ah-5h+h^2}{h}=[/tex]
[tex]2a-5+h[/tex]
