Problem 20 (1996 AJHSME)

Suppose there is a special key on a calculator that replaces the number currently displayed with the number given by the formula $\frac{1}{1-x}$. For example, if the calculator is displaying $2$ and the special key is pressed, then the calculator will display $-1$ since $\frac{1}{1-2}=-1$. Now suppose that the calculator is displaying $5$. After the special key is pressed $100$ times in a row, the calculator will display