\[\boxed{\text{5.541.}}\]
\[\textbf{а)}\ 5\ :\frac{2}{3} = 5 \cdot \frac{3}{2} = \frac{15}{2} = 7\frac{1}{2}\]
\[\textbf{б)}\ \frac{3}{8}\ :\frac{1}{3} = \frac{3}{8} \cdot 3 = \frac{9}{8} = 1\frac{1}{8}\]
\[\textbf{в)}\ \frac{1}{12}\ :\frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{3}{5}\]
\[\textbf{г)}\ \frac{14}{55}\ :\frac{5}{21} = \frac{14}{55} \cdot \frac{21}{5} = \frac{294}{175} =\]
\[= 1\frac{19}{175}\]
\[\textbf{д)}\ \frac{121}{234}\ :\frac{11}{12} = \frac{121}{234} \cdot \frac{12}{11} =\]
\[= \frac{11 \cdot 6}{117 \cdot 1} = \frac{11 \cdot 2}{39} = \frac{22}{39}\]