5. (5 points) As shown in the figure, $\angle 1=\angle 2=\angle 3=\angle 4=\angle 5=\angle 6=30^{\circ}$, then the sum of all acute angles in the figure is $\qquad$ .
【Analysis】From the figure, we can see that there are 6 acute angles formed by a single angle, $\angle 1=\angle 2=\angle 3=\angle 4=\angle 5=\angle 6=30^{\circ}$; there are 5 acute angles formed by two angles: $\angle 1+\angle 2 ; \angle 2+\angle 3 ; \angle 3+\angle 4 ; \angle 4+\angle 5 ; \angle 5+\angle 6$, each of which has a degree of $30^{\circ}+30^{\circ}=60^{\circ}$; the angles formed by three angles are no longer acute but right angles; therefore, there are a total of 11 acute angles in the figure, 6 of which are $30^{\circ}$ and 5 of which are $60^{\circ}$. By adding them all up, we can solve the problem.

【Solution】Solution: According to the analysis, the sum of all acute angles in the figure is: $30^{\circ} \times 6+60^{\circ} \times 5$
$$
\begin{array}{l}
=180^{\circ}+300^{\circ} \\
=480^{\circ} .
\end{array}
$$

Answer: The sum of all acute angles in the figure is $480^{\circ}$.
Therefore, the answer is: $480^{\circ}$.