5. On the plane, there is a set of points $M$, the coordinates $x$ and $y$ of which are related by the equation

$$
\sin (3 x+4 y)=\sin 3 x+\sin 4 y
$$

A circle of radius $R$, located on the same plane, does not intersect the set $M$.

What values can the radius of such a circle take?
Answer: $R \in\left(0 ; \frac{\pi}{6}\right)$