My daughter sounds very similar to yours. She gets very frustrated and I have to tell her "we are taking a break from this, we will try again after snack" or after a movie, or whatever. The other day she just couldn't cut out a princess crown the same way her teacher does. After 5 wasted pieces of paper, I took it away, set it on the table, and put on a movie. In my bustle of getting the movie on (and pretending to ignore her tantrum), she decided on her own that one of the previous ones would do, got it off the table, and I could hear her say "I'm trying, not crying." Apparently her school had taught her this mantra and she frequently uses it now whenever she's trying to do something that may become frustrating. I think taking the frustrating object out of the picture and me not babying her frustrations (which only feeds them) helped her realize she needed to solve the problem and calm down on her own. (BTW, I'm a child behaviorist in profession, so the tactics I use at work influence how I deal with my own daughter.) Make sure that you're giving HUGE social praise whenever she completes a difficult task without becoming frustrated, especially if she accepts that it's okay if it's not perfect, as well as when she plays with kids and obeys instructions from adults. Kids learn to do what we praise them for doing. One child I'm working with has perfectionism issues, and we have made him a book using construction paper and pictures/text off the computer that says "I like to do things exactly the right way, but sometimes I try and try and it still isn't right. I try not to get frustrated, but when I do, I can take a break and play outside, watch a movie, play with my favorite toy, etc. The last page says "my my mom, dad, teacher (whoever) are so proud of me when I stay calm!" with real pics of mom, dad, teacher, and some balloons. it's really cute, if you have the time to make it and then you can read it to her daily and it will help her (before she's frustrated) to learn how to cope.
Two important developmental tasks for five-year-olds are honing their peer relationship skills and learning how to manage frustraition. Your granddaughter is having problems with these, as well as withaccepting the jurisdiction of adults. The involvement with her peers is imprtant, particularly because she is an only child, but even if she had siblings the out-of-school peer contact would be important. It's only through such 'practice' that she will get better. When children are without siblings at home, they don't have the benefit of the many thousands of interactions that occur among children who are siblings - these help pave the way for relationships outside of the family. Managing situations that are frustrating for her requires learning some skills: recognizing the signs of frustration, stopping what she is doing, taking a break, calming down, etc. These are all normal tasks of development for her age. Her parents might chat with her teacher and see if he/she can convey some of the tactics the teacher employs in the classroom to help children with such reactions. Another avalable resource might be the guidance person at her school.