Answer
$2a+h-5$.
Work Step by Step
The given function is
$f(x)=x^2-5x+3$
Plug $x=a+h$.
$f(a+h)=(a+h)^2-5(a+h)+3$
Use the algebraic identity $(a+b)^2=a^2+2ab+b^2$ and simplify.
$f(a+h)=a^2+2ah+h^2-5a-5h+3$
Now plug $x=a$.
$f(a)=a^2-5(a)+3$
Simplify.
$f(a)=a^2-5a+3$
The required expression is
$=\frac{f(a+h)-f(a)}{h}$
Substitute all values.
$=\frac{a^2+2ah+h^2-5a-5h+3-(a^2-5a+3)}{h}$
Clear the parentheses.
$=\frac{a^2+2ah+h^2-5a-5h+3-a^2+5a-3}{h}$
Add like terms.
$=\frac{2ah+h^2-5h}{h}$
Simplify.
$=2a+h-5$.