jmc

There are $\left(\genfrac{}{}{0ex}{}{10}{2}\right)=45$ ways to choose two members of the group, and there are $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$ ways to choose two girls. Therefore, the probability that two members chosen at random are girls is $\frac{10}{45}=\boxed{\frac{2}{9}}$.