5. If $f(a+b)=f(a) \cdot f(b)$, and $f(1)=1$, then the value of the expression $\frac{f(2)}{f(1)}+\frac{f(3)}{f(2)}+\cdots+\frac{f(2005)}{f(2004)}$ is
A. 2003
B. 2004
C. 2005
D. Cannot be determined
5. B Let $b=1, f(a+1)=f(a) \cdot f(1)=f(a)$, thus $\frac{f(2)}{f(1)}=\frac{f(3)}{f(2)}=\cdots=\frac{f(2005)}{f(2004)}=1$.