According to the question,

In 5 days A can complete$=\frac{1}{15}\times 5=\frac{1}{3}$^rd of the work

Remaining work $=1-\frac{1}{3}=\frac{2}{3}$

In one day (A+B) can complete$=\frac{1}{15}+\frac{1}{10}=\frac{2+3}{30}=\frac{5}{30}=\frac{1}{6}$^th of the work

∴ $\frac{2}{3}$ ^rd of the work will be finished by (A+B) in $\frac{2}{3}\times 6$ days that is in 4 days.

∴ Total time taken= (5+4) days =9 days.

 Hence option D is the correct.