5. If $A: B=1 \frac{2}{3}: 4 \frac{5}{6}, C: A=2 \frac{1}{5}: 3 \frac{2}{3}$, then $A: B: C$ expressed in the simplest integer ratio is
5. If $A: B=1 \frac{2}{3}: 4 \frac{5}{6}, C: A=2 \frac{1}{5}: 3 \frac{2}{3}$, then $A: B: C$ expressed in the simplest integer ratio is $\qquad$ 10: $29: 6$.

【Solution】Solution: $A: B$
$$
\begin{array}{l}
=1 \frac{2}{3}: 4 \frac{5}{6} \\
=\frac{5}{3}: \frac{29}{6} \\
=\left(\frac{5}{3} \times 6\right):\left(\frac{29}{6} \times 6\right) \\
=10: 29
\end{array}
$$
$$
\begin{array}{l}
C: A \\
=2 \frac{1}{5}: 3 \frac{2}{3} \\
=\frac{11}{5}: \frac{11}{3} \\
=\left(\frac{11}{5} \times 15\right):\left(\frac{11}{3} \times 15\right) \\
=33: 55 \\
=3: 5 \\
=6: 10
\end{array}
$$

This way, the parts of $A$ are all 10,
so $A: B: C=10: 29: 6$.
Therefore, the answer is: 10: 29: 6.