You misunderstand Matthew 12:5, and present an incorrect question, for you have removed it from the surrounding context. Let's see all three renditions in Matthew, Mark and Luke, in context.
[1] What day was it? It was the 7th day, the Sabbath (Matthew 12:1,2,8; Mark 2:23,24,27,28; Luke 6:1,2,5)
[2] Who was accusing whom? The Pharisees, since they didn't directly accuse Jesus, they accused His disciples (Matthew 12:2; Mark 2:24; Luke 6:2) by asking Jesus about their actions.
[3] What were the disciples doing, that the Pharisees accused them? They were walking out in nature, through a grain field, and became hungry and took some grain to eat (Matthew 12:1; Mark 2:23; Luke 6:1).
[4] Was it lawful, or unlawful to pluck grain on sabbath, in a field, and eat it? It was lawful (Deuteronomy 23:24-25).
So the pharisees were not following 'the Law' (ie 'Moses') as it was written, but were accusing, based upon their own man-made regulations, and said what the disciples were doing was 'not lawful' (Matthew 12:2; Mark 2:24; Luke 6:2).
[5] How did Jesus respond to the Pharisees mistaken accusation? Jesus first provided the example of 'King' David (Matthew 12:3-4; Mark 2:25-26; Luke 6:3-4), followed by the 'priests' serving in the Temple to God (Matthew 12:5-6). This means Jesus spoke of the King-Priests, a holy royal nation of priests, which the disciples also were, who were serving Jesus (King, Priest, and greater Temple) in ministry on sabbath.
[6] Jesus is using their (pharisees) definition of 'unlawful' against them, and cites the scriptures in opposition to their oral tradition. God was merciful to David, his men and their need, when they were being persecuted for serving God by others, just as the Pharisees were doing to Jesus and the disciples right then. Additionally, Jesus is not saying that the priests in the Temple were actually desecrating the sabbath, but was using their (Pharisees) personal definition against them. The priests were actually "blameless". The Sabbath day, and command of God (Exodus 20:8-11) say that the sabbath is for Holy purpose ("to keep it holy", requires doing something, a holy work), and serving God in the temple, and keeping the body temple in service by eating on time when hungry is no sin, or violation of the actual command and Law of God (10 C).
[7] Jesus reiterates the innocence (non-sinful actions) of the disciples by saying, "But if ye had known what this meaneth, I will have mercy, and not sacrifice, ye would not have condemned the guiltless." (Matthew 12:7). Notice, Jesus states that the Pharisees had "condemned" the disciples who were "guiltless". In other words, the Pharisees were 'fault-finding', looking for any excuse to accuse the innocent. They were murderers breaking sabbath by accusing, as their father the devil does, and would rather the disciples suffer, simply to get at their LORD, MASTER - Jesus. He was their real target.
[8] The sabbath was made for the service of mankind (since the time of Adam the first, and especially for all in Adam the last, since the sabbath was really made for Jesus, and all in Him; Col 1:16; Mar. 2:27). There is nothing in the command of God (Exodus 20:8-11) that says a man (person of mankind) cannot eat from the field upon the sabbath day. The final phrase, and texts to follow, show that Jesus was not negating sabbath keeping, or justfying sinful actions, but was showing the Pharisees what actual sabbath keeping was like. He was giving rest back to the sabbath for them all, exemplifying how it ought to be kept by all. The Pharisees had loaded the sabbath down with a near endless list of man-made regulations, which in practice, actually caused people to transgress God's law (10 C).
Mat 12:1 At that time Jesus went on the sabbath day through the corn; and his disciples were an hungred, and began to pluck the ears of corn, and to eat.
Mat 12:2 But when the Pharisees saw it, they said unto him, Behold, thy disciples do that which is not lawful to do upon the sabbath day.
Mat 12:3 But he said unto them, Have ye not read what David did, when he was an hungred, and they that were with him;
Mat 12:4 How he entered into the house of God, and did eat the shewbread, which was not lawful for him to eat, neither for them which were with him, but only for the priests?
Mat 12:5 Or have ye not read in the law, how that on the sabbath days the priests in the temple profane the sabbath, and are blameless?
Mat 12:6 But I say unto you, That in this place is one greater than the temple.
Mat 12:7 But if ye had known what this meaneth, I will have mercy, and not sacrifice, ye would not have condemned the guiltless.
Mat 12:8 For the Son of man is Lord even of the sabbath day.
Mar 2:23 And it came to pass, that he went through the corn fields on the sabbath day; and his disciples began, as they went, to pluck the ears of corn.
Mar 2:24 And the Pharisees said unto him, Behold, why do they on the sabbath day that which is not lawful?
Mar 2:25 And he said unto them, Have ye never read what David did, when he had need, and was an hungred, he, and they that were with him?
Mar 2:26 How he went into the house of God in the days of Abiathar the high priest, and did eat the shewbread, which is not lawful to eat but for the priests, and gave also to them which were with him?
Mar 2:27 And he said unto them, The sabbath was made for man, and not man for the sabbath:
Mar 2:28 Therefore the Son of man is Lord also of the sabbath.
Luk 6:1 And it came to pass on the second sabbath after the first, that he went through the corn fields; and his disciples plucked the ears of corn, and did eat, rubbing them in their hands.
Luk 6:2 And certain of the Pharisees said unto them, Why do ye that which is not lawful to do on the sabbath days?
Luk 6:3 And Jesus answering them said, Have ye not read so much as this, what David did, when himself was an hungred, and they which were with him;
Luk 6:4 How he went into the house of God, and did take and eat the shewbread, and gave also to them that were with him; which it is not lawful to eat but for the priests alone?
Luk 6:5 And he said unto them, That the Son of man is Lord also of the sabbath.
[1] What day was it? It was the 7th day, the Sabbath (Matthew 12:1,2,8; Mark 2:23,24,27,28; Luke 6:1,2,5)
[2] Who was accusing whom? The Pharisees, since they didn't directly accuse Jesus, they accused His disciples (Matthew 12:2; Mark 2:24; Luke 6:2) by asking Jesus about their actions.
[3] What were the disciples doing, that the Pharisees accused them? They were walking out in nature, through a grain field, and became hungry and took some grain to eat (Matthew 12:1; Mark 2:23; Luke 6:1).
[4] Was it lawful, or unlawful to pluck grain on sabbath, in a field, and eat it? It was lawful (Deuteronomy 23:24-25).
Deu 23:24 When thou comest into thy neighbour's vineyard, then thou mayest eat grapes thy fill at thine own pleasure; but thou shalt not put any in thy vessel.
Deu 23:25 When thou comest into the standing corn of thy neighbour, then thou mayest pluck the ears with thine hand; but thou shalt not move a sickle unto thy neighbour's standing corn.
So the pharisees were not following 'the Law' (ie 'Moses') as it was written, but were accusing, based upon their own man-made regulations, and said what the disciples were doing was 'not lawful' (Matthew 12:2; Mark 2:24; Luke 6:2).
[5] How did Jesus respond to the Pharisees mistaken accusation? Jesus first provided the example of 'King' David (Matthew 12:3-4; Mark 2:25-26; Luke 6:3-4), followed by the 'priests' serving in the Temple to God (Matthew 12:5-6). This means Jesus spoke of the King-Priests, a holy royal nation of priests, which the disciples also were, who were serving Jesus (King, Priest, and greater Temple) in ministry on sabbath.
[6] Jesus is using their (pharisees) definition of 'unlawful' against them, and cites the scriptures in opposition to their oral tradition. God was merciful to David, his men and their need, when they were being persecuted for serving God by others, just as the Pharisees were doing to Jesus and the disciples right then. Additionally, Jesus is not saying that the priests in the Temple were actually desecrating the sabbath, but was using their (Pharisees) personal definition against them. The priests were actually "blameless". The Sabbath day, and command of God (Exodus 20:8-11) say that the sabbath is for Holy purpose ("to keep it holy", requires doing something, a holy work), and serving God in the temple, and keeping the body temple in service by eating on time when hungry is no sin, or violation of the actual command and Law of God (10 C).
[7] Jesus reiterates the innocence (non-sinful actions) of the disciples by saying, "But if ye had known what this meaneth, I will have mercy, and not sacrifice, ye would not have condemned the guiltless." (Matthew 12:7). Notice, Jesus states that the Pharisees had "condemned" the disciples who were "guiltless". In other words, the Pharisees were 'fault-finding', looking for any excuse to accuse the innocent. They were murderers breaking sabbath by accusing, as their father the devil does, and would rather the disciples suffer, simply to get at their LORD, MASTER - Jesus. He was their real target.
[8] The sabbath was made for the service of mankind (since the time of Adam the first, and especially for all in Adam the last, since the sabbath was really made for Jesus, and all in Him; Col 1:16; Mar. 2:27). There is nothing in the command of God (Exodus 20:8-11) that says a man (person of mankind) cannot eat from the field upon the sabbath day. The final phrase, and texts to follow, show that Jesus was not negating sabbath keeping, or justfying sinful actions, but was showing the Pharisees what actual sabbath keeping was like. He was giving rest back to the sabbath for them all, exemplifying how it ought to be kept by all. The Pharisees had loaded the sabbath down with a near endless list of man-made regulations, which in practice, actually caused people to transgress God's law (10 C).
