Length of $C_4$: $\frac{8}{27}$.

Length of $C_5$: $\frac{16}{81}$.

Length of $C_n$: ${\left(\frac{2}{3}\right)}^{n-1}$.

As $n$ tends to infinity, this tends to 0. The Cantor set does indeed have length 0 (once you've introduced a suitable notion of "length"!).