Staircase Nim

Coins sit on a staircase numbered step 0 (the ground) up to step 4, with counts (step 0..4) = (2, 3, 1, 0, 5). A move takes any positive number of coins from a step s >= 1 and moves them down to step s-1. Coins on step 0 are off the board. The player who cannot move (all coins on the ground) loses. Under optimal play, does the first player win or lose?