Equal shares of a treasure

A treasure of coins is shared among some heirs in order. Heir $1$ takes $1$ coin and then $\frac{1}{5}$ of the coins left after that. Heir $2$ then takes $2$ coins and $\frac{1}{5}$ of the coins left after that, and in general heir $k$ takes $k$ coins and then $\frac{1}{5}$ of what remains. All shares are whole numbers, every heir receives the same amount, and the treasure is used up exactly. The treasure has more than $1$ coin. How many coins were in the treasure?

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