An experiment consists of tossing 7 fair (not weighted) coins, except one of the 7 coins has a head on both sides. Compute the probability of obtaining exactly 5 heads.

Step 1 ：An experiment consists of tossing 7 fair (not weighted) coins, except one of the 7 coins has a head on both sides. We are asked to compute the probability of obtaining exactly 5 heads.

Step 2 ：We can divide the problem into two cases. Case 1: The two-headed coin is among the 5 heads. Case 2: The two-headed coin is not among the 5 heads.

Step 3 ：For case 1, we need to choose 4 heads from the remaining 6 coins (which are fair), and the remaining 2 coins will be tails.

Step 4 ：For case 2, we need to choose 5 heads from the remaining 6 coins (which are fair), and the remaining 1 coin will be a tail, and the two-headed coin will also be a tail.

Step 5 ：The total number of outcomes when tossing 7 coins is \(2^7\), but since one coin is two-headed, the total number of outcomes is \(2^6\).

Step 6 ：We can calculate the probability for each case and then add them together to get the final probability.

Step 7 ：Let's correct this and calculate the probability again.

Step 8 ：The total number of outcomes is \(2^6 = 64\).

Step 9 ：For case 1, the number of outcomes is \(\binom{6}{4} = 15\).

Step 10 ：For case 2, the number of outcomes is \(\binom{6}{5} = 6\).

Step 11 ：The probability is \(\frac{15+6}{64} = 0.328125\).

Step 12 ：Final Answer: The probability of obtaining exactly 5 heads when tossing 7 coins, one of which has heads on both sides, is \(\boxed{0.328125}\).