Do you always rub your hands? Can she possibly be 'feeding off' of your anxiety and feeling insecure or unsafe because of it? Kids can pick up on the smallest things, especially from their mothers at that age. You don't usually hear of 5 year olds getting more anxious then is typical for that age. But if they feel insecure in their surroundings or uncertain with their primary caregiver then that's a different story.
It may be more likely that your GAD is making you more compulsive or obsessive over your child and making 'a mountain out of a mowhill' where you should not be overly concerned.
Let your child be a child and perhaps be around other children more often. Don't sweat the small stuff with her or she'll too become overly concerned about them.
Keep in mind that my advice comes from one who let his wife do everything when it came to raising our daughters...so take it for what that's worth! :-)
It's time to address other reasons for your daughter's tingling in her hands. If all other causes are ruled out and they determine it's anxiety, then get her into therapy so that you can nip this in the bud while she is still young. Anxiety can and does cause this, but she's so young to have anxiety this severe, and that is why you must rule out all other causes first, and there are many. Her pediatrician should not brush this off as anxiety! But if everything is okay get her into a child psychologist for an evaluation and go from there. It's more important than ever now, for you to not let your daughter see your anxiety. At this age they pick up on everything and I know you don't want to see her going thru this. It doesn't make any sense either that her doctor would think this would just go away in a few weeks, even if it is anxiety, it won't just go away. The cause of her anxiety would need to be addressed first and then this dealt with. Have all other causes ruled out immediately. Good luck and take care.