Not the smallest piece of the Law has ever been abolished. But its summary, and its fulfillment, is its command to love my neighbor as myself. If I love myself as I should, and love others in the same way, I will fulfill the Law. But I must come to Jesus to be taught the way of love and to be given the power to love as he does. Then he will fulfill the whole Law through me, in the love he shows others through my life.

You tube video link: Not Abolishing the Law But Fulfilling It.
Going one paragraph farther back in the context of Matthew 5:23-24, I find the following discussion of the relationship between Jesus, his followers, and the Law of Moses:

On a quick reading, this paragraph sounds as if it is saying that to be a follower of Jesus who will be honored in his Kingdom, I must keep the Law even more scrupulously than the scribes and Pharisees of Jesus’ day. The Pharisees took pride in not only keeping the Law to the letter, but also keeping perfectly a long list of other traditional rules designed, they thought, to keep them as far as possible from breaking any of the commands of the law!
But, looking more carefully at what Jesus said, he did not command me to keep the law more strictly than the Pharisees. What he said was that he would “fulfill” (or complete) and “accomplish” the Law:

So the Law remains. It has not been abolished. It continues and will continue to have application to me until it is fulfilled and the objectives for which it was given are accomplished.
But it will not be fulfilled in the way the scribes and Pharisees thought. It will not be fulfilled by making it an end in itself, the reason for which I live, and therefore being very careful never to neglect even a single detail of it. My righteousness before God, does not come from scrupulously keeping the details of the Law while ignoring its purpose.
No, the fulfillment of the Law that Jesus came to show, and to give, us, fulfills its purpose, which, as Paul later wrote, is to show us how to love each other:

Not the smallest piece of the Law has ever been abolished. It still shows me how I should respond to God and treat myself and others. But its summary, and its fulfillment, is its command to love my neighbor as myself. If I love myself as I should, and love others in the same way, I will not harm them. And I will have completely fulfilled the Law.
Of course it is true, as is often said, that I am not able to do this perfectly. Acting only in my own strength and wisdom, I will sometimes disregard the needs and welfare of others and will harm them. In doing so, I will break one of the commandments of the Law, which exists at least in part to make it clear to me that the harm I did is a sin before God. I will be convicted by the Law, and my own conscience, as a lawbreaker, and incur guilt. But if I understand my guilt correctly, I will know that I am guilty not because of the detail of the Law that I failed to observe, but because I acted contrary to love.
The solution to this is not to simply ignore the Law–or Jesus’ amplification of it here in his Sermon on the Mount–but to learn what they are teaching me. That is, I must learn that I cannot fulfill the Law’s demands on my own. I cannot fulfill the Law by perfectly keeping the Law of Love on my own. I must come to Jesus to be taught the way of love and to be given the power to love as he does. Then he will fulfill the whole Law through me, in the love he shows others through my life.
Applying this to the command to go and be reconciled in verses 23 and 24 is fairly simple. If I am holding a grudge against my brother or sister, a fellow believer in Christ, and so dehumanizing them, treating them as less worthy of my love and care than others, as described in the last article, I am quite obviously acting contrary to love. And if I know that I have offended a brother or sister, and so put them at risk of dehumanizing me, and so committing murder against me in their heart, my love for them demands that I do what I can to reconcile with them. I must do what I can to make the offense right, to keep them from going down the destructive path of holding a grudge against me.
So Jesus’ command to go and be reconciled has never been abolished or superseded. And Jesus did not give the command only to show that I can’t keep it. I cannot ignore it and still fulfill the Law of Love. Instead, Jesus intends to fulfill the command through me. I must come to him for wisdom to know how to keep it and power to do what he shows me. And I must trust him to bring reconciliation in his own way and time when I obey his command. But I am to obey the command!