$3 l+2 m+n=0$ ...(1)
and $2 m n-3 n l+5 m l=0$ ...(2)
$$
\begin{aligned}
& \Rightarrow n(2 m-3 l)+5 m l=0 \Rightarrow n=-(2 m+3 l) \\
& \therefore \quad-(2 m+3 l)(2 m-3 l)+5 m l=0 \\
& \Rightarrow 9 l^2-4 m^2+5 m l=0 \\
& \Rightarrow 9 l^2+5 m l-4 m^2=0 \\
& \Rightarrow 9\left(\frac{l}{m}\right)^2+5\left(\frac{l}{m}\right)-4=0
\end{aligned}
$$

If $\frac{l}{m}=t$ then $9 t^2+5 t-4=0$
$$
\begin{aligned}
& \Rightarrow 9 t(t+1)-4(t+1)=0 \Rightarrow t=-1, \frac{4}{9} \\
& \Rightarrow \frac{l}{m}=-1 \Rightarrow l=-m \\
& \because n=-(2 m+3 l)=-(2 m-3 m)=m
\end{aligned}
$$
$\therefore \quad t: m: n=-m: m: m=-1: 1: 1$
Also for $\frac{l}{m}=\frac{4}{9} \Rightarrow l=\frac{4 m}{9}$
$$
\begin{aligned}
& n=-(2 m+3 l)=-\left(2 m+\frac{4 m}{3} a\right)=\frac{-10 m}{3} \\
& \therefore \quad l: m: n=\frac{4 m}{9}: m: \frac{-10 m}{3} \\
& \Rightarrow l: m: n=4: 9:-30 \\
& \therefore \quad \text { Angle between lines }=\left|\frac{-4+9-30}{\sqrt{1^2+1^2+1^2} \cdot \sqrt{4^2+9^2+30^2}}\right| \\
&=\left|\frac{-25}{\sqrt{3} \cdot \sqrt{997}}\right|=\frac{25}{\sqrt{2991}} .
\end{aligned}
$$