5. Given $f(x)=3 \sin \left(2 x+\frac{\pi}{3}\right)$, which of the following options is correct? ( ).
A. $f(3)>f(1)>f(2)$
B. $f(3)>f(2)>f(1)$
C. $f(1)>f(3)>f(2)$
D. $f(2)>f(1)>f(3)$
5. A
$$
f(1)=3 \sin \left(2+\frac{\pi}{3}\right), f(2)-3 \sin \left(4 \cdot \frac{\pi}{3}\right), f(3)-3 \sin \left(6+\frac{\pi}{3}\right)
$$

Since $-\frac{\pi}{3} \approx 1$, so $f(1) \approx 3 \sin \pi \approx 0$, $f(2) \approx 3 \sin \frac{5 \pi}{3} = -\frac{3\sqrt{3}}{2}$.
$f(3) \approx 3 \sin \left(2 \pi+\frac{\pi}{3}\right) \approx 3 \times \frac{\sqrt{3}}{2}$. Therefore, $f(3)>f(1)>f(2)$.