5. Find the range of values for the function $y=f(x)=\frac{3+\cos x}{2-\sin x}$.
5. Let $u=\cos x, v=\sin x$, then $l: u+y v+(3-2 y)=0, \odot O: u^{2}+v^{2}=1$, given that $l$ intersects $\odot O$, we have $\frac{|3-2 y|}{\sqrt{1+y^{2}}} \leqslant 1$, which simplifies to $3 y^{2}-12 y+8 \leqslant 0$, solving this yields $2-\frac{2 \sqrt{3}}{3} \leqslant y \leqslant 2+\frac{2 \sqrt{3}}{3}$.