5. The complex number $z$ satisfies $|z|(3 z+2 i)=2(i z-6)$, then $|z|$ equals

保留了源文本的换行和格式。
5. 2

Analysis: Let $r=|z|$, then the original equation can be transformed into: $12+2 r i=2 i z-3 r z$, so $2 \sqrt{36+r^{2}}=r \sqrt{9 r^{2}+4}$, yielding $r=2$.