Your answers seem to have fallen into two very different camps - one the "leave her alone" and the other "fix this now!" I don't know which is right for your daughter. My daughter too is very shy, and I was concerned for her. At the same time, I didn't want her to think that there was something "wrong" with her, as a) I love her how she is and b) shyness is one of the most pronounced traits a person can have from birth.
I talked to a child psychologist just to get some suggestions, because what I was doing to help her be more comfortable wasn't helping. To me, that was key - she wasn't shy and happy, she was shy and clearly nervous around people. That's not a good feeling. What the psychologist told me was so counterintuative, but has worked wonders. Before we go someplace where there are going to be a lot of people, or a few people she doesn't know, I say "there are going to be a lot of people, and that's going to make you really scared. You're going to get that funny feeling in your stomach. That's okay, but you need to remember that you'll have a lot more fun if you decide to talk to people." I also clearly lay out how much I'm going to let her cling to me. I say something like, "My friends are going to be there too. Its fine if you want to eat dinner with me, but I'm going to be talking to the grown-ups" or "I will stay inside the birthday party with you for 10 minutes, but after that I have to make a phone call so I'll have to step out of the room. You can either keep playing with everyone else or you can sit off to the side. You'll have more fun if you play with everyone else, but it's your choice."
What the psychologist told me, and what makes perfect sense, is that my daughter is/was not only shy, but was being totally rocked by the "out of control" feeling that she was getting when around a big group. I mean, everyone else was mingling/talking/playing, why was this so hard for her? And that reinforced the shy feeling, because she felt paralyzed. By helping her prepare for the "yucky" nervous feeling, she could get over it. It has helped soooo much. My daughter's still pretty shy, but she doesn't stick to me like glue anymore. She'll occasionally talk to adults in a big gathering. She'll almost always talk to kids at a party. We just had to help her change her pattern of self-talk from paralysis to "I can do this."
You might as well try it with your daughter. It's very accepting of who she is, but also recognizes that, at 5, she needs to be part of the process of making herself happy. You can't always make her comfortable, she needs to learn how to do that on her own.
Good luck!