So the expectation here is that the new 5 yr old girl ingrain herself into an already established group of kids? Yikes, that is asking a LOT! It's hard for an adult to do, much less a soft natured child.
I agree with those who have said the focus here needs to be the established group. Those kids need to learn a valuable lesson of making an effort to include everyone and have empathy for the new kid. The established group should be taught to see how the new girl might feel (y'know teaching compassion) and make an extra effort to be kind and inclusive.
If the group is already too clicky maybe each parent who is interested can invite the girl and her mother for an individual play date at their home. This would give the kids a chance to get to know each other one-on-one and not be so stressful for the new kid. I'm not sure I agree with Rhonda. If the kids are already clicky they will just ignore her at her house too and play with all her toys without her, probably making her feel even worse.
The ownership here is on the established group to make the new kid (and her mom, for that matter) feel welcome.