$$4\frac{3}{5}=\frac{4 \cdot 5 + 3}{5}=\frac{20+3}{5}=\frac{23}{5}$$
$$4\frac{3}{5}:\frac{5}{23}=\frac{23}{5}:\frac{5}{23}=\frac{23}{5} \cdot \frac{23}{5}=\frac{23 \cdot 23}{5 \cdot 5}=\frac{529}{25}=21\frac{4}{25}$$
Ответ: $$21\frac{4}{25}$$