For the expression `(ab)*ba` I came up with the following (very poorly drawn):

[![DFA](https://i.stack.imgur.com/AhDP9.png)](https://i.stack.imgur.com/AhDP9.png)

However, this was not the correct answer - apparently the solution requires five states. I don't understand why my DFA doesn't describe the expression. My interpretation of the expression is "`ab` any number of times, followed by `ba`". Is this correct?