Does this DFA describe this regular expression? For the expression (ab)*ba I came up with the following (very poorly drawn):



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?
For something to be a DFA, it should have transitions from every state for every letter in the alphabet. Your alphabet is {$a, b$}, so every state should have a transition for $a$ as well as $b$, e.g., your state 2 does not have a transition for $a$. Complete your DFA and you'll get what is that 5th state that you are missing.