Union Government
(1) The President shall hold office for a term of five years from the date on which he enters upon his office: Provided that - (a) the President may, by writing under his hand addressed to the Vice-President, resign his office; (b) the President may, for violation of the Constitution, be removed from office by impeachment in the manner provided in article 61; (c) the President shall, notwithstanding the expiration of his term, continue to hold office until his successor enters upon his office.
The President serves a five-year term, but can resign early (by writing to the Vice-President), can be impeached and removed for violating the Constitution, and continues in office past the official end of the term until a successor actually takes over - so there is never a gap with no President in office.
If a presidential election is delayed for any reason, the sitting President continues performing all duties of the office until the newly elected President is sworn in - the country is never left without a President.