computation first:
f(x) is given in the question
to get f(x+h), just replace every "x" with "x+h"
$\displaystyle f(x+h) = 3(x+h)^2 + 5(x+h)=3x^2 + 6xh + 3h^2+5x+5h$
so:
$\displaystyle f(x+h) - f(x) =3x^2 + 6xh + 3h^2+5x+5h-3x^2 -5x$
cancel out and then divide by h to finish.