What is the LAW according to Matthew 5:19

Therefore whoever relaxes one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven, but whoever does them and teaches them will be called great in the kingdom of heaven. 20 For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven.

The Preceding versus read:

17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly, I say to you, until heaven and earth pass away, not an iota, not a dot, will pass from the Law until all is accomplished.

Jesus has come to fulfill the law , not to “abolish” the Law. The Law condemned all who approached it before, stopping their mouths from self righteousness. NO HUMAN was ever justified by the law.

19 Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. 20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. - Ro 3:19–20.

The Law:

Mosaic Law? Ten Commandments

Abolish: ( loosen down; disintegrate; demolish; halt; destroy; dissolve; be guest; lodge; come to nought; overthrow; throw down).

Fullfill: (execute; finish; verify; coincide; accomplish; after, (be) complete; end; expire; fill (up); fulfil, (be; make) full (come); fully preach; perfect; supply)

Jesus does what no man could do, he “Completes” the Law, he perfects the law, with his life on earth. He is sinless and has accomplished what no man can do. He did not come to destroy the law and choose to live lawlessy telling people to follow his example, but he fulfilled (completed, accomplished, perfected) the law and was the forerunner of our faith.

where Jesus has gone as a forerunner on our behalf, having become a high priest forever after the order of Melchizedek-  Heb 6:20.

So if Jesus accomplishes the LAW how is it applicable to his followers if we are called to follow him?

Is the law then against the promises of God? Certainly not! For if there had been a law given which could have given life, truly righteousness would have been by the law. 22 But the Scripture has confined all under sin, that the promise by faith in Jesus Christ might be given to those who believe. 23 But before faith came, we were kept under guard by the law, [f]kept for the faith which would afterward be revealed. 24 Therefore the law was our [g]tutor to bring us to Christ, that we might be justified by faith. 25 But after faith has come, we are no longer under a tutor. - Galatians 3:25

Why do we no longer need a guardian or tutor? The law has condemned us all, so that we could be FREELY given the gift and promise of Jesus Christ’s justification by faith, in short, have been justified by faith (Not by the Law or Accomplishment of the Law) when we believe or are “brought to Christ”. It seems like the Spirit of Truth (Holy Spirit) is now our “Tutor” in a sense, guiding us to all Truth.

But when He, the Spirit of Truth (the Truth-giving Spirit) comes, He will guide you into all the Truth (the whole, full Truth). For He will not speak His own message [on His own authority]; but He will tell whatever He hears [from the Father; He will give the message that has been given to Him], and He will announce and declare to you the things that are to come [that will happen in the future]. John 16:13

Jesus did not put away the LAW but through his sacrifice we are justified by Faith and the Holy Spirit has empowered us to do the following (Which allows us to “achieve the Law and Prophets) if we follow these two commandments.  

37 Jesus replied: “‘Love the Lord your God with all your heart and with all your soul and with all your mind.’[c] 38 This is the first and greatest commandment. 39 And the second is like it: ‘Love your neighbor as yourself.’[d] 40 All the Law and the Prophets hang on these two commandments.”