Matthew 5, does not approve a remarriage. But does authorize divorce for sexual immorality. Divorce does not mean your free to marry again.
32 But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery.
Again Paul teaches, the only acceptable reason for another marriage is death of the spouse.
1 Corinthians 7
39 A wife is bound by law as long as her husband lives; but if her husband dies, she is at liberty to be married to whom she wishes, only in the Lord.
This here people use to justify another marriage if there exists a living former spouse, but its twisting scriptures by saying the believing spouse is not under bondage in this case where the unbeliever departs. Not under bondage is not referring to the original marriage's falling apart allowing for another marriage, Paul is authorizing a peaceful separation, they are not under an emotional bondage to reconcile with the departing spouse. AND Paul moves on to say you may save your HUSBAND OR WIFE in such cases, Paul still calls them husband and wife!
1 Corinthians 7
12 But to the rest I, not the Lord, say: If any brother has a wife who does not believe, and she is willing to live with him, let him not divorce her. 13 And a woman who has a husband who does not believe, if he is willing to live with her, let her not divorce him. 14 For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy.
15 But if the unbeliever departs, let him depart; a brother or a sister is not under bondage in such cases. But God has called us to peace. 16 For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife?