Five Rational Pirates

Five perfectly rational pirates, ranked $1$ (lowest) to $5$ (highest), must split $100$ gold coins. The highest-ranked surviving pirate proposes a split; all pirates, including the proposer, vote, and the proposal passes with at least half the votes. If it fails, the proposer is thrown overboard and the next-highest-ranked pirate proposes. Each pirate values survival first, then personal gold, then (when indifferent) seeing others thrown overboard. Find the number of coins the original proposer (rank 5) keeps in the outcome reached under this reasoning.