A proposal to increase the number of seats on the board of library trustees from three to five may be initiated in either of the following alternative ways:
(a) By a petition signed by registered voters residing within the library district equal in number to at least 5 percent of the total number of votes cast in the library district at the last preceding general state election at which a Governor was elected, and filed with the supervising board of supervisors of the library district.
(b) By a resolution adopted by the board of trustees and filed with the supervising board of supervisors.