"We believe that a man must be called of God, by prophecy, and by the laying on of hands by those who are in authority, to preach the Gospel and administer in the ordinances thereof"
In our church, everybody gets what we call a calling. It can range from a bishop, the spiritual leader of the congregation, to a music director. Callings in the church are varied in individual responsibility and difficulty. But they all have one thing in common, all callings are extended from God. The apostle Paul said of the priesthood that "no man taketh this honour unto himself, but he that is called of God" (Hebrews 5:4). This principle applies with all callings in the church. You'll never see anybody petitioning to be the bishop. There's no elections to decide church leadership. The will of God prevails; He leads this church and through His servants, the callings are extended.
That "authority" mentioned in the fifth article of faith refers to the priesthood. That authority is necessary for any calling to be extended. Whether it be the President of the church or a teacher in Sunday school, all positions in our church are "called... by those who are in authority". These callings are not accepted blindly though, all are encouraged to pray and know for themselves the will of God. Every child of God has that right.
I know that Christ's church has been restored! His gospel is on the earth! The Church of Jesus Christ of Latter-Day Saints is set up exactly how God wants it to be. I know that Christ lives and that Thomas S. Monson is His prophet.
For more on the Articles of Faith, see http://mormon.org/articles-of-faith/.