Mr. Patrick is preparing a five-question true-false quiz for his class. He flips a coin before writing the first question. If it is heads, he writes a true statement and if it is tails, he writes a false statement. He continues this until all five statements are written. What is the probability that the correct sequence of answers is TFTFT ? Express your answer as a common fraction.
Since all sequences of 5 answers are equally likely, the probability of any given 5-answer sequence is simply $\frac{1}{2^5}$, since each answer is equally likely to be true or false. So, the answer evaluates to $\frac{1}{2^5} = \boxed{\frac{1}{32}}$.