smc

Let the first term be $a$ and the common ratio be $r$. Therefore, the second term is $ar$, the fourth term is $a{r}^3$, and the fifth term is $a{r}^4$. We're given that $a{r}^4-a{r}^3=576⟹a{r}^3(r-1)=576$ and $ar-a=9⟹a(r-1)=9$. Dividing this first equation by this second one, we get $r^3=\frac{576}{9}=64⟹r=4$. Therefore, $a(4-1)=9$, so $a=3$. Therefore, the first five terms of this series are $3,12,48,192,768$, and their sum is $1023,\boxed{1023}$.