OMM 2001 Problem 6

A collector of rare coins has coins of denominations $1, 2,..., n$ (several coins for each denomination). He wishes to put the coins into $5$ boxes so that: (1) in each box there is at most one coin of each denomination; (2) each box has the same number of coins and the same denomination total; (3) any two boxes contain all the denominations; (4) no denomination is in all $5$ boxes. For which $n$ is this possible?