Write five numbers which you cannot decide whether they are square just by

A number whose unit digit is 2, 3, 7 or 8 cannot be a perfect square.

On the other hand, a number whose unit digit is 1, 4, 5, 6, 9 or 0 might be a perfect square although we have to verify that.

Applying these two conditions, we cannot determine whether the following numbers are squares just by looking at their unit digits:

1111, 1001, 1555, 1666 and 1999