Most likely position of the fifth king in a shoe

A shoe of $10$ shuffled standard decks has $520$ cards, $40$ of which are kings. Cards are turned over one by one from the top, and the game stops when the fifth king appears. You win if your guess for the total number of cards turned (counting that fifth king) is the right one. Which number gives you the highest chance of being exactly right? (This is the mode, not the mean.)

$54$. The fifth king is at position $k$ with probability proportional to $\binom{k-1}{4}\binom{520-k}{35}$. The ratio of consecutive terms exceeds $1$ exactly when $k(485-k)>(k-4)(520-k)$, i.e. $k<2080/39\approx53.3$, so the probabilities rise up to $k=54$ and fall afterwards.