若定义在$\mathbf{R}$上的函数$f(x)=\sin\omega x+\cos\omega x(\omega>0)$的图象在区间$[0,\pi]$上恰有5条对称轴，则$\omega$的取值范围为
$\text{A.}$ $\left[\dfrac{17}{4},\dfrac{21}{4}\right)$
$\text{B.}$ $\left(\dfrac{17}{4},\dfrac{25}{4}\right)$
$\text{C.}$ $\left[\dfrac{17}{4},\dfrac{25}{4}\right)$
$\text{D.}$ $\left[\dfrac{33}{4},\dfrac{41}{4}\right)$