Which coin?

In front of you are two identical-looking coins. One of them is fair (it comes up Heads 50% of the time), while the other is unfair, in that it comes up Heads 75% of the time. You take one of the coins and flip it five times, yielding the following sequence: HTHTH. The probability that the coin you've been flipping is the unfair one can be written as \(\frac{m}{n}\), where m and n are positive coprime integers. Find \(m+n\).

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