The Reformers were resolute in reducing the number of Sacraments from seven to two. I believe Luther held to three Sacraments at one point: baptism, confession, and the Eucharist. But he eventually reduced the number to two, thus setting the standard for magisterial Protestantism.
My suspicion is that the "other five" were cut not because they were not biblical but because they ultimately wanted to cut loose of the Priesthood (Holy Orders) and the necessity of sacramental confession (Penance).
Baptism and the Eucharist are obviously the most important Sacraments and it's easier to support these biblically.
The magisterial Protestants essentially defined a Sacrament in the Catholic way, "an outward sign of an invisible grace, instituted by Christ." Penance was denied sacramental status because it apparently had no outward sign. Confirmation was denied sacramental status because it is difficult to establish the outward sign (chrism or hands?) and it's hard to find a dominical saying of Christ explicitly establishing it. Marriage is a creation ordinance so it isn't necessarily "instituted by Christ," though this can be debated.
But there are two that are pretty hard to dismiss. Ordination was obviously something that Christ instituted. He chose twelve and gave them special instructions. It's also clear that the outward sign, beginning at Pentecost was the laying on of hands.
The real problem for Protestants, as I see it, is the Sacrament of Holy Unction. It has an outward sign: anointing with oil. It has an inward grace: healing and forgiveness. It was definitely instituted by Christ and we see the Apostles doing it in the Gospels:
Mark 6:13 They drove out many demons and anointed many sick people with oil and healed them.
Unction of the Sick clearly meets all the specifications of Protestants, so why is it not granted the status of Sacrament? Could a LowChurcher out there explain this?
I also once read that St Thomas (Episcopal) Church 5th Ave in Manhatten has seven windows commemorating the "Seven Sacraments," though not by that title. There is a window for Baptism, Confirmation, Communion, Marriage, Ordination, Confession & Absolution, and...Prayer. Apparently they were so resistent to the idea of Holy Unction that they swapped it for the rite of "Prayer." I just can't understand this. Why is Unction so bad? I think I'm safe in saying that not even the 1662 Book of Common Prayer contains a rite for Unction. This seems shortsighted given the instructions of St James:
James 5:14 Is any one of you sick? He should call the presbyters of the church to pray over him and anoint him with oil in the name of the Lord.