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Решение:

$$\begin{gathered} 1)\frac{13}{15}-1\frac{5}{6}=\frac{13}{15}-\frac{1\cdot 6+5}{6}=\frac{13}{15}-\frac{11}{6}=\frac{13\cdot 2-11\cdot 5}{30}=\frac{26-55}{30}=\frac{-29}{30}=-\frac{29}{30} \\ 2)1\frac{4}{25}:(-\frac{29}{30})=\frac{1\cdot 25+4}{25}:(-\frac{29}{30})=\frac{29}{25}:(-\frac{29}{30})=-\frac{29}{25}\cdot \frac{30}{29}=-\frac{30}{25}=-\frac{6}{5}=-1\frac{1}{5}=-1,2 \end{gathered}$$

Ответ: –1,2.