Cat, your poor daughter, what a horrible thing to happen.
As others have said, bones heal well, and hopefully the movement will come back in her fingers. It will all take time, and it may be that the hospital will support her recovery with physio.. Her arm will be weak when she comes out of plaster, but they regain strength very quickly.
I think people on here are reacting to your friends shouting 'sue' , rather than you. As you say, you are simply asking an opinion of your friends' advice.
As you now know suing is something that happens IF there has been wrongdoing/ negligence.
I am worried about your little girl's phrase 'she wasn't holding on properly ' and whether she is getting upset because the questioning makes her think she is to blame. She needs to know that 'accidents just happen ' too.
It may be that the equipment was too high, not aimed at 5 year olds, or too many kids were using it at once, or it may be that she just fell in an awkward way: you do need to look into the accident report.
I hope she regains her confidence very soon.