What does Matthew 15:5 mean?

In response an accusation that His disciples don't follow a tradition about handwashing, Jesus is leveling a counter-charge. The Pharisees who attack Jesus for ignoring a human tradition are guilty of using human traditions to ignore actual commands of God!

The example Jesus has raised is the fifth of the Ten Commandments: Honor your father and mother (Exodus 20:12). He also adds the follow-up from Exodus 21:17, that anyone who speaks evil against his parents must be put to death. These commands both came to Israel directly from God through Moses. They reveal how seriously the issue of honoring one's parents was to God for His people.

From God's perspective, one of the ways that children were expected to honor their parents was to care for them as they aged. This may have included paying expenses for them or taking aging parents into their own home to live with them. Jesus is showing that God expected the Israelites to care for their parents in this way.

Religious leaders such as the Pharisees, however, had a tradition which allowed for someone to declare that some of their possessions or money were korban, meaning a gift devoted to God. This is the spiritual equivalent of a tax write-off: a way to shield resources from being taken for some other purpose. That loophole in tradition apparently allowed such a person to continue to hold on to these valuable items and make use of them. Alternatively, they could claim the goods were devoted to God—as of today—then later annul the vow. In this way, they could avoid the responsibility to care for parents either to save the cost or because of resentment.

In stern terms, Jesus calls out the Pharisees. He not only criticizes them for hypocrisy, but also for enabling those under their instruction permission to openly violate the clear intention of God's original command. He says they allow for people to tell their parents, "What you would have gained from me is given to God."