Contradiction with Matthew 10:5-6
Jesus instructs his disciples not to go to the Gentiles or Samaritans, while Acts 13:5 involves preaching to non-Jews.
Matthew 10:5-6: These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into [any] city of the Samaritans enter ye not:
Contradiction with Acts 26:20
Paul recounts preaching first to Jews and then Gentiles, whereas Acts 13:5 focuses on preaching to Jews.
Acts 26:20: But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea, and [then] to the Gentiles, that they should repent and turn to God, and do works meet for repentance.
Contradiction with Galatians 2:9
Paul acknowledges a division of labor, with Peter to the Jews and himself to the Gentiles, but Acts 13:5 shows him preaching to Jews.
Galatians 2:9: And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we [should go] unto the heathen, and they unto the circumcision.
Contradiction with Romans 11:13
Paul refers to himself as the apostle to the Gentiles, yet Acts 13:5 involves him preaching to Jews.
Romans 11:13: For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
Contradiction with 1 Corinthians 1:22-24
Paul describes Jews as seeking signs and Greeks seeking wisdom, contrasting with preaching primarily to Jews in Acts 13:5.
1 Corinthians 1:22-24: For the Jews require a sign, and the Greeks seek after wisdom: