5. \(\frac{\left(15:\frac{5}{18}:3\frac{3}{8}\right)\cdot\left(-\frac{1}{16}\cdot\frac{11}{36}\cdot\frac{5}{48}\cdot18\right)}{\left(8\frac{21}{22}-11\frac{5}{11}\right):1\frac{2}{3}}\)

Сначала вычислим числитель:

\[15:\frac{5}{18}:3\frac{3}{8}=15\cdot\frac{18}{5}:\frac{27}{8}=54\cdot\frac{8}{27}=16.\]

\[16\cdot\left(-\frac{1}{16}\cdot\frac{11}{36}\cdot\frac{5}{48}\cdot18\right)=-\frac{55}{96}.\]

Теперь вычислим знаменатель:

\[\left(8\frac{21}{22}-11\frac{5}{11}\right):1\frac{2}{3}=\left(\frac{197}{22}-\frac{126}{11}\right):\frac{5}{3}=\left(\frac{197}{22}-\frac{252}{22}\right)\cdot\frac{3}{5}=-\frac{5}{2}\cdot\frac{3}{5}=-\frac{3}{2}.\]

\[\left(-\frac{55}{96}\right):\left(-\frac{3}{2}\right)=\frac{55}{96}\cdot\frac{2}{3}=\frac{55}{144}.\]

Ответ: \(\frac{55}{144}\).