According to the question,

In 1 day,

A man and his friend can complete $\frac{1 }{3}$^th of the work

Man can complete $\frac{1}{5}$^th of the work

His friend can complete the work$=\frac{1}{3}-\frac{1}{5}=\frac{2}{15}$

∴ His friend can complete the work in $\frac{15}{2} or 7\frac{1}{2}$days.

Hence option C is the correct.