5. As shown in the figure, the three interior angles of a triangle are $(5 x+3 y)^{\circ} 、(3 x+20)^{\circ}$ and $(10 y+30)^{\circ}$, where $x 、 y$ are positive integers, then $x+y=$ $\qquad$ .
【Analysis】According to the sum of interior angles 180 degrees:
$$
\begin{aligned}
5 x+3 y+3 x+20+10 y+30 & =180 \\
8 x+13 y & =130 \\
y & =10-\frac{8}{13} x
\end{aligned}
$$

Since they are all positive integers, $x=13, y=2$, the sum is 15