Sec. 6. The department of local government finance shall, within a reasonable time, fix a date for a hearing on the petition filed under section 5(b) of this chapter. The hearing shall be held in a county in which the library district is located. The department of local government finance shall notify:
(1) the library board; and
(2) the first ten (10) taxpayers whose names appear on the petition;
at least five (5) days before the date fixed for the hearing.