5. If $\theta \in\left(0, \frac{\pi}{2}\right), f(\theta)=\cos \theta+\theta \sin \theta$, then among the following judgments
(1) $f(\theta)>1$,(2) $f(\theta)1$; there also exists $\theta$, such that $f(\theta)<1$, the correct sequence number is $\qquad$ .
5. (1).

Given $\theta \in\left(0, \frac{\pi}{2}\right)$, we know $\cos \theta>\cos ^{2} \theta, \theta>\sin \theta$. Therefore, $f(\theta)>\cos ^{2} \theta+\sin \theta \cdot \sin \theta=1$.