The problem with issues like table manners is twofold: first, you want your children to behave appropriately; but second, you also want your children to choose to behave appropriately. Teaching the first is not all that difficult; punishments, delivered appropriately, will certainly yield a result eventually.
Teaching the second, however, won't necessarily come with punishments. Your child will need to learn why she needs to behave in that manner, and that reason is not "because I told you so". The reason is complicated, but ultimately comes down to a combination of "wanting to satisfy your nutritional needs", "society expects you to act in a certain way", "family time is important", etc.; but even there, you need her to understand those as well, and to decide to value those things (at least some). A five year old likely doesn't completely understand why it's important to eat a balanced meal, doesn't really get why she should follow societal norms, and doesn't care much about family time.
We struggle with this some with our three year old, probably as much as any other parents do I suspect. How we deal with this, is twofold.
First, when we ask him to come to dinner and he resists, we remind him why we're asking him. Then, we also provide him a reason to want to cooperate. This isn't always ideal, because I'd rather him cooperate because of the good reasons inherent in the activity - but it does help reinforce the activity, which is good in itself. This is basically how the conversation goes, except it often stops earlier than the last line; as he grows older and matures, we hope to see it become internal largely, where he understands all of these whys.
R, please come to dinner, it's dinnertime.
I don't want to have dinner.
I know, but it's important that you eat dinner so you aren't hungry, and so you grow up big and strong.
I don't want to have dinner. I'm not hungry.
Okay, but we still eat dinner together at the table so we can spend some time together. Besides, you might like some of what we made.
I don't want to have dinner. I want to play.
I know, and I love you, but everyone needs to sit together just for a little while. Why don't you come pick out which plate and fork you want to use?
I want Cars fork.
And now he's at the dinner table. Also works is "What drink do you want" and "Do you want to help serve?" from time to time (if it's something he can help with at his age). We do sometimes have discussions about some of the 'why' questions above - 'Why do we eat together', 'Why do I need to eat to grow up big and strong', etc.; if he asks, we have a (short) discussion about it. He's only 3, but he already has a pretty decent understanding of some of this.
We would use a few techniques that are not exactly positive, if needed; particularly, 'no playing with toys during dinner', and the final alternative to dinner is going directly to bed (which is used only if
I'm too sick is the reason - if you're truly sick, you should go to bed early, and in the few cases he's been willing to do that, I believe he probably was happier that way). But overall, we try to keep it positive as much as possible, because that will lead (hopefully!) to more buy-in on his part.
The major advantage of trying to get buy-in as opposed to using punishments to enforce behavior is that she will choose to behave this way when not around you more easily. It also allows her to develop her own personality more - while at 5 or 6 you probably don't have much opportunity to choose to participate (or not) in socially appropriate behavior, as she gets older she should have some choice here - so long as she has a concrete understanding of what that choice means. As an adult it took me years to learn to eat anything with my hands, because I'd been trained to not do so: so eating fried chicken with my hands was a difficult task for quite a few years, because it took me a long time to undo the 'training' that it was just wrong to eat that way; anything not on a bread product was off limits entirely. I learned over time what was appropriate and not, and why - but you can help your daughter learn this at a younger age, and should.
More explanation of this basic strategy towards child rearing is available in several books, including Parent Effectiveness Training. The basic concept is avoiding punishments, and instead teaching your child - even from an extremely young age - why you're asking him or her to do whatever you're asking.