Markov Chains & Long-Run Behavior · Superchallenge problem

A stack of $5$ cards is shuffled by repeating this step: take the top card off and insert it back into the stack at one of the $5$ possible places (back on top, between any two of the other cards, or at the bottom), chosen uniformly. What is the expected number of steps until the card that started at the bottom is first on top? Express your answer as a common fraction.