Answer
$$f'\left( 5 \right) = 42$$
Work Step by Step
$$\eqalign{
& {\text{let }}f\left( x \right) = 3g\left( x \right) - 2h\left( x \right) + 3 \cr
& {\text{find the derivative}} \cr
& f'\left( x \right) = {D_x}\left( {3g\left( x \right) - 2h\left( x \right) + 3} \right) \cr
& {\text{use the sum rule for derivatives}} \cr
& f'\left( x \right) = {D_x}\left( {3g\left( x \right)} \right) - {D_x}\left( {2h\left( x \right)} \right) + {D_x}\left( 3 \right) \cr
& {\text{use multiple constant rule for derivatives}} \cr
& f'\left( x \right) = 3{D_x}\left( {g\left( x \right)} \right) - 2{D_x}\left( {h\left( x \right)} \right) + {D_x}\left( 3 \right) \cr
& {\text{solve derivatives}} \cr
& f'\left( x \right) = 3g'\left( x \right) - 2h'\left( x \right) \cr
& {\text{evaluate }}f'\left( 5 \right) \cr
& f'\left( 5 \right) = 3g'\left( 5 \right) - 2h'\left( 5 \right) \cr
& {\text{substitute }}g'\left( 5 \right) = 12{\text{ and }}h'\left( 5 \right) = - 3 \cr
& f'\left( 5 \right) = 3\left( {12} \right) - 2\left( { - 3} \right) \cr
& {\text{simplifying}} \cr
& f'\left( 5 \right) = 42 \cr} $$
