There is more turn-taking required in gym and it is important that children listen to instruction as there are safety implications and that can typically be a challenge for young children. I actually think it is a good thing for them to learn though and probably improves their performance in school because those are valuable learning behaviours. I have worked as an assistant coach with young children and you definitely do see them improve in physical competence. One thing I really like about gym are that you have to put a bit of work in to progress but if you do you are pretty much assured of incremental improvement. So I think you learn to earn your achievements and feel proud of them. Also because it is basically an individual sport you don't all have to be doing the same thing at the same time. That makes it relatively easy to adapt for different levels of ability across a class and integrate kids with special needs. It also means there is less opportunity for direct comparison between different kids which I think encourages gymnasts to focus on their own progress rather than comparing themselves with others.
Most gym classes and probably dance classes too will let you do a first session free before you have to commit to paying for a block of classes. I'd recommend taking advantage of that because it really comes down to a question of what your daughter enjoys and within gym or within dance some classes are going to be better run than others.
If you are sat at the side of the class make sure you don't get too loud talking to other parents or allow bags or shoes to spill into the working area and don't call to your child. I have seen that happen in classes sometimes and I think parents sometimes just do that without thinking and don't realize how much they are undermining the discipline and respect for the gym environment coaches try to instil in children (and which is important to keep them safe.) It is not like military discipline stuff but just that they need to listen to instructions, concentrate when they are doing gymnastic activity, be aware of what is going on around, not distract others and not muck about on equipment unsupervised.
For a 5-year-old... Gymnastics for sure!
Dance is wonderful. But for younger kids, it's not as much fun. There's a lot of standing in one spot for long periods - either at a ballet barre, in a line, or out on the floor while the teacher walks around correcting each student. For most 5-year-olds, that's pretty boring... which is why the majority of girls this age wind up quitting. Gymnastics, on the other hand, is very active and allows kids to do what they naturally love to do: jumping, climbing, swinging and flipping. 5-year-olds have a lot of energy, and most kids can't wait to go to gym... where they're actually encouraged to do all the things they aren't allowed to do at home or at school. And gymnastics is not only fun, but it has sooo many benefits. Whether she sticks with it long-term or just does it for a few years, the all-around strength, flexibility, coordination, courage and self-confidence she'll develop will give her a huge advantage in any other sport or activity she later pursues.
Definitely start with gymnastics. She can always try dance when she's a little older, when she'll be more mature and better prepared for the discipline it requires. And if she's had a background in gymnastics, the dance moves will come so much easier for her. She'll be one of the best in the class, she'll progress more quickly, and she'll probably enjoy it a whole lot more than she would now.
P.S. This reminded me of a video that cracked me up: http://www.wimp.com/firstposition/
I did gymnastics as a little kid and ballet for two years when i was older. I'd say gymnastics, but I'm slightly partial. There's lots of different parts that your child could get involved in (rope, floor, trampoline, bars...) and it'd keep your child active and trying new things.
Dance is good too, and would help provide some sort of musical know-how. If you want a more 'dance-y' gymnastics you could always have your child do gymnastics then pick up rhythmic gymnastics, the type you see in the Olympics where they have a prop (ribbon, ball...) and almost gracefully dance/move with it as they do stunts. They also say gymnastics helps with dance as it improves flexibility... I'd say gymnastics as its harder to pick up while dance is slightly easier too at an older age.
In my personal opinion, gymnastics. As a child I took both and benefited more from gymnastics as it improved coordination, flexibility, strength, and also dancing skills!
A Dancer has to do gymnastics sometimes too!
I am wanting to put my 5 year old in either Dance or Gymnastics but not sure which one? Does anyone have advice on which one might be better for a 5 year old that has never had any type classes before?