A set of five quarters was marked with a permanent marker. A random English language letter was written on the face of each coin. On the back of each coin, a different random English language letter was written. All of the letters written on the coins are upper-case.

Each of the five quarters was marked using the same process, so it is possible to have duplicate letters within the set of five coins. No coin has the same letter written on both sides.

After marking the coins, they are placed in an opaque cloth bag. You reach into the bag and select a coin using a blind draw. Once selected, you flip the coin and place it on a table. You repeat this process for each coin, drawing it at random from the cloth bag, flipping it, and then placing it on the table. You do not have any special coin-flipping skill; the coin flip causes a random side of the coin to be selected. After the coins have all been drawn and flipped, the coins are arranged in a neat row in the order in which they were drawn.

Suppose you were hopeful that the result would spell the word "HELLO" after the selection and flipping process was completed. Furthermore, suppose that by random chance the marking of the coins coincidentally maximized the odds that you would get a favorable outcome. Keep in mind that the order in which the coins are drawn from the bag is still entirely random.

In this favorable scenario, what is the probability that the letters on the coins spell the word "HELLO"?

(please limit your response for this question to N in M, where N and M are integers, as a reduced fraction. For example, if the correct answer is 2/10, your answer would be 1 in 5)