If you look at just the first 5 dice and compute the probability that player one rolls lowest, of the 6^4 combinations of rolls the other players can make: 1 be

If you look at just the first 5 dice and compute the probability that player one rolls lowest, of the 6^4 combinations of rolls the other players can make: 1 beats all 6^4; 16 beats 4^4, 17 beats 4^4, 32 beats 2^4, 33 beats 2^4, and 48 beats nothing. So player 1 is lowest 1840 out of 6^5, or ~23.7%. A similar argument shows player 5 rolls lowest 1414 out of 6^5, or only 18.2% of the time. I don't have a good intuitive explanation though.