Originally Posted by maki
He's scared of her and terrified of making a mistake.
You may wish to acquaint him with ideas such as "learning from our mistakes" and "Done is better than perfect." This old post on perfectionism may be of interest, ongoing.

Originally Posted by maki
He says she yells all the time (I'm guessing she isn't actually yelling at 5 year olds?)
...
She said she doesn't think she's ever yelled at him.
I take this as a confession by the teacher that she yells in class. IMO, this is inappropriate. You may wish to check your State Laws and school policies regarding classroom management, student discipline, and other related topics. It is possible that a law and/or policy is being violated.

Originally Posted by maki
... he was stressing that his teacher said he couldn't go to recess if he didn't finish his drawing in time. I brought that up with her this morning and she said that she didn't say that.
In a polite and engaging manner, you may want to ask your child several probing questions such as... remember when you told me that the teacher said you could not go to recess if you did not finish your drawing in time....? Was she speaking just to you...? To a group of kids...? To the class in general? Where was she... standing... sitting...? Did you look at her...? Who was she looking at...? You, specifically...? Or looking all around...? Or not at a person...? What else was she doing when she said this?

Once you understand whether the teacher was standing over him and specifically addressing him... or giving directions to the class in general while absent-mindedly muti-tasking... or trying to keep other kids focused on their own work while she worked with a particular student... you will have a better set of facts to work with.

In a safe place at home, you may want to begin a dated log or journal with notes about the classroom incidents and their impact upon your child. You may want to occasionally ask the teacher polite, open-ended questions to help you gather information from her perspective about what occurred. If warranted in the future, you may want to carefully choose a small selection of these incidents which you have documented, to discuss in requesting a classroom change so that your child has a different teacher.

Here is a roundup on advocacy.