Well, this one's interesting. First off, it's incredibly common that kids turning five have a turn for the worse with their behavior. It's all about an increased awareness of what's expected of them at that age, and therefore, performance anxiety. However, I've never heard it expressed in this anxious manner before.
Although, if she tends to express her stress via anxiety, I guess this could be considered normal for her.
Try discussing common things that kids learn how to do at this age, and figure out if she's afriad she won't be able to accomplish them. Learning to read, ride bike, whistle, go to school, move up at Sunday school, etc. What you may find is, as she accomplishes these things one by one, she'll relax and realize her fear was overblown. She'll become a confident five-year-old.
If, during the next difficult stage of her life, she hasn't outgrown this extreme anxious reaction to stress, I might suggest taking her to a behavioral psychologist, so that she can learn how to tone down her stress reaction. Otherwise, she'll keep reacting like that everytime something goes wrong (Dad loses a job, Grandma dies, etc.).