The term, five-fold ministry, has come into popular use, but you will not find the term in the Bible.  The five-fold ministry is a way of referring to Ephesians 4:7, 8, 11 "But to every one of us is given grace according to the measure of the gift of Christ. Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts to men. And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;"

The five-fold ministry refers to apostles; and some, prophets; and some, evangelists; and some, pastors and teachers.  Some church leaders who do not believe this part of Scripture will avoid talking about the five-fold ministry in any form.  Often you will hear this verse about the five-fold ministry read as something like this: "And he gave some pastor-teachers."

Technically, this is not a five-fold ministry.  There is an office, that of the apostle.  Apostles can be either elders, such as Paul or Peter or deacons, such as Timothy or Titus.  There are four ministries mentioned: prophets, evangelists, pastors, and teachers.

The five-fold ministry was restored to the church in the great move of the Spirit which began in 1948 in Northern Canada and still continues today.  Many counterfeits have sprung up, but the Spirit of God is moving throughout the Earth.

For detailed information about the five-fold ministry and apostles in the church, see Apostles