A can complete $\frac{1}{3}$ of a work in 5 days and B, $\frac{2}{5}$ of the work in 10 days, In how many days both A and B together can complete the work?

The part of the work done by A in one day is $\frac{1}{3}·\frac{1}{5}=\frac{1}{15}$

The part of the work done by $B$ in one day is $\frac{2}{5}·\frac{1}{10}=\frac{1}{25}$

The part of the work done by both A and B together is $\frac{1}{15}+\frac{1}{25}=\frac{5+3}{75}=\frac{8}{75}$

The number of days that both together A and B together to complete the work is $\frac{75}{8}$ days.