Except as otherwise provided by this code, a political party's nominees in the general election for offices of state and county government and the United States Congress must be nominated by primary election, held as provided by this code, if the party's nominee for governor in the most recent gubernatorial general election received 20 percent or more of the total number of votes received by all candidates for governor in the election.

A political party is entitled to have the names of its nominees placed on the ballot, without qualifying under Subsection (a), in each subsequent general election following a general election in which the party had a nominee for a statewide office who received a number of votes equal to at least five percent of the total number of votes received by all candidates for that office.