Heads, tails, and what else?

In front of you are two identical-looking coins. One is a standard fair coin, but the other one is a very special kind of coin, characterized as follows:

1. There is always an equal probability of heads or tails.
2. On the $\textrm{n}^{\textrm{th}}$ flip, there is a $1 - \frac{1}{n}$ probability that the coin will land on its side !

You do not know which is which, so you pick up one of them randomly, and then you flip it 5 times.

The probability that you will be able to identify the special coin given 5 flips can be expressed as $\frac{a}{b}$ where $a$ and $b$ are coprime positive integers. Find $a + b$ .