I will use Sub-Game Perfect Nash Equilibrium as a solution concept and solve the game by backwards induction (also known as Zermelo's algorithm).
In the last decision nodes of the game tree (round 4), there are only two pirates left. If the youngest pirate vote against the offer, he will get everything and and the oldest will be thrown overboard. Clearly the youngest is voting against the proposal if he does not get everything. If the proposal gives everything to the youngest pirate, he is indifferent between accepting or rejecting it (we already have least two equilibria!). Let's consider the case where the youngest votes for the proposal if he gets everything. In this case, the proposer offer everything to the youngest who then accepts it.
In the last but one nodes of the tree (round 3), there are only three pirates left. Clearly, the second youngest pirate strictly prefers to vote for any proposal that gives him any coins and is indifferent between voting for or against any proposal that gives him zero coins. So again we may have multiple equilibria. Let's consider the case he always votes for the proposal. In this case, the proposer offers zero to all the others and the proposal is accepted.
So in round 2, the proposer (the 2nd pirate) knows the 3rd pirate will require at least all the coins to vote for the proposal but both the 4th and 5th pirate will vote for any proposal that gives them any coins. Thus, the best he can do is to offer one coin to each of the 4th and 5th pirates and zero to the 3rd.
Finally, in round 1, the proposer knows the second pirate requires at least 48 coins to vote, the third requires at least zero, the forth and fifth require at least one each.
So the first pirate will propose (47,0,1,1,1).
In sum, there is at least one subgame-perfect Nash equilibrium where the division proposed is (47,0,1,1,1) and all but the second pirate vote in favor. You can check the other cases (breaking the ties/indifferences in different ways) but for sure there are other equilibria (perhaps with similar payoffs).
This is a cute game, it reminds a bit "Hungry Lions" but with voting added.