5. Given that the generating function of a sequence is $f(t)=\left(t+t^{2}+t^{3}+\cdots\right)^{n}$, then the coefficient of $t^{r}$ in its expansion is ( )
A. $C_{r}^{n}$
B. $C_{r-1}^{n} \quad$
C. $C_{r}^{n-1}$
D. $C_{r-1}^{n-1}$
5. D $\left(t+t^{2}+t^{3}+\cdots\right)^{n}=t^{n}(1-t)^{-n}=t^{n} \sum_{r=0}^{\infty} C_{n+r-1}^{r} t^{r}=\sum_{r=n}^{\infty} C_{r-\eta}^{r-1} t^{r}=\sum_{r=n} C_{r-1}^{n-1} t^{r}$.