Here, $f(x)$ is linear. It means that $f(x)$ represents a straight line. So $(-2,29)$ and $(3,39)$ are the two points on this line.
Therefore, the equation of the line is $$y-29=\left(\frac{39-29}{3-(-2)}\right)\left (x-(-2) \right)$$
[As we know $y-y_1=m(x-x_1)$ where $m$ is the slope and $m=\frac{y_2-y_1}{x_2-x_1}$]
$$\Rightarrow y=2(x+2)+29=2x+33\\ \therefore f(x)=2x+33$$
So at $x =5$, $f(5)=2(5)+33=43$.
The answer is 43.