That's very likely a big part of the issue - the end of nursing can leave a child feeling very vulnerable. But another part is purely that she's 5. It's a delicate age - she's out of the toddler years but not "a big kid" yet, not really. She's starting to have a sense of the wider world around her, but that's scary! It's a big world! So it's really normal for her to want to keep tabs on her safety net, her mom, and to keep mommy close.
>>Here is the issue: she is so attached to me that she will sometimes cry if she cannot come with me<<
What kind of crying are we talking about? Inconsolable screaming and flailing around? Is she crying so much she's getting sick or wearing herself out? Or does she weep a little and then settle down and get on with her day once you're out of sight? It's an important question because, while naturally you don't want to hurt her feelings, it's also perfectly normal for her to be upset and express that via tears. Life has real limits - real sources of frustration, disappointment, and sadness. And 5yos are often very sensitive to frustration, disappointment and sadness Because they're beginning to get a sense of the wider world. It's not uncommon for 5yos to cry because they want to fly to the moon - not pretend to fly, not go up in a balloon or airplane, but really fly to the moon. And it's impossible. And it's okay to cry about that, to be disappointed at the edges of possibility.
Be gentle with her feelings, but also recognize that it's okay for her to feel and express them - even when they're not comfortable. One of the things she's getting a chance to learn about is emotions - negative as well as positive. How nice that she can do that with people who are sweet and kind and will try to help her, rather than being sent away someplace where her feelings are inadmissible and a kind of failure.
>> But now at play groups or at the park, etc she will not go and play without me right there.<<
It's also important to recognize that what you've done in the past may not always be workable - kids' needs change! And it's important that your parenting changes along with them. Right now, it may not be feasible for you to get work done while she's playing outside the home. Time to change the way you get work done! It might be better to plan less outings so that you can schedule more work time at home, or rearrange how you and your husband divvy up the available work-hours.
Any advice on how to encourage her to do things on her own but still respect her feelings?
"Encouraging" her to do things without you is much more likely to make her more anxious about wanting to be close to you. In fact, with the end of nursing, it's better to plan to spend more time with her for awhile, reassuring her as much as possible by your close presence. Again, that might entail less outings - it sounds like you're out of the house a huge amount, with art and dance classes! Cut down to one or two outings a week, including things like running errands and shopping. Your daughter is letting you know that she's feeling vulnerable right now. Help her feel secure by doing a lot of nesting.