Explanation:

- Under the Mines Act, 1952, the Special Officer has a right to enter any mine for surveying, levelling, and measuring purposes.

- However, this cannot be done arbitrarily; prior notice must be given to the Manager.

- The law specifies the minimum number of days for such advance notice.

- Option 1 (Three days): This is NOT the correct period.

- Option 2 (Five days): This is the correct answer. A Special Officer must provide at least five days' prior notice to the mine manager.

- Option 3 (Seven days): The Act does not specify a seven-day notice for this purpose.

- Option 4 (Fourteen days): Fourteen days’ notice is not mandated in such cases by the Act.

Option 2, Five days, is correct.