jmc

This is a geometric series with 5 terms, a first term of $1/3$, and a common ratio of $-1/3$. The sum of this series is $\frac{\frac{1}{3}-\frac{1}{3}\cdot (-\frac{1}{3}{)}^5}{1-(-\frac{1}{3})}=\frac{\frac{1}{3}+(\frac{1}{3}{)}^6}{1+\frac{1}{3}}=\boxed{\frac{61}{243}}$.