Pretty much all Nim games can be solved by starting at the end and working backwards.
Let's first solve the basic Nim, with only one pile, and simple actions (take 1-4). Let's enumerate the endgame situations by how many sticks are left, and see what kind of pattern emerges:
Rules: 2 players, one pile, take 1-4, taking last wins
0: loss, cannot take
1. Four players
In the four players case, regardless of what D says, C can make a statement to secure arbitrarily high surviving probability for themself. There're many ways C can do that, one of which is like the following:
2. Five players
The above analysis for 4 players gives us a leverage to handle the 5 players case. Notice that if E makes the ...
If the first player is the one who says either 2nd January or 1st February, then the winning player is
The first player
The strategy is to
Note: I assumed that the game only goes over one year. If players can go on to the next January, then