What is the remainder when the positive integer ~$n$~ is divided by 5?

1. When ~$n$~ is divided by 3, the quotient is 4 and the remainder is 1.

2. When ~$n$~ is divided by 4, the remainder is 1.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.