No person shall be eligible to the office of Governor or Secretary of State unless he shall have attained the age of thirty years at the time of his election, nor to the office of Attorney-General unless he shall have attained the age of twenty-five years at the time of his election, and have been admitted to practice in the Supreme Court of the Territory or of the State of Utah, nor unless he shall be in good standing at the bar at the time of his election. No person shall be eligible to any of the offices provided for in section one of this article, unless at the time of his election he shall be a qualified elector, and shall have been a resident citizen of the State or Territory for five years next preceding his election. The State Auditor and State Treasurer shall be ineligible to election as their own successors.