Matthew 10:5-6 concerns the beginning of Jesus’ ministry. At the end of Chapter 9, Jesus sees that the multitudes have increased, coming to him to be healed of their infirmities. Seeing that the “harvest is great but the laborers are few”, in chapter 10, he “deputizes” the 12 Apostles and sends them forth to preach, to heal the sick and to cast out demons. He does limit their preaching, etc., to the lost sheep of the House of Israel.
However, this was only a temporary command, as Matthew 28:16-20 supercedes the command of Matthew 10:5-6.
***16 And the eleven disciples went into Galilee, unto the mountain where Jesus had appointed them. 17 And seeing them they adored: but some doubted. 18 And Jesus coming, spoke to them, saying: All power is given to me in heaven and in earth. 19 Going therefore, teach ye all nations; baptizing them in the name of the Father, and of the Son, and of the Holy Ghost. 20 Teaching them to observe all things whatsoever I have commanded you: and behold I am with you all days, even to the consummation of the world.***
We now see that Jesus has commanded the Apostles to teach all nations, not just the Israelites.
I also refer you to Acts 10 and 11:1-18. Peter is convinced through the vision given him and the subsequent events concerning Cornelius, that God had commanded that the Gentiles be evangelized. Through the vision, God again commands that all nations be taught the Gospel, superceding Matthew 10:5-6.
See post #58. The Israelites were world wide (sifted through the Nations) [Amos 9:9] by this time and that is where He sent the Twelve! If he meant they were to evangelize the Gentiles....why was Paul, twenty years later, still saying his (Peter's) mission was to the circumcised [Galatians 2:7-8]?
I also refer you to Acts 10 and 11:1-18. Peter is convinced through the vision given him and the subsequent events concerning Cornelius, that God had commanded that the Gentiles be evangelized.
Peter was not sent to evangelize Cornelius [Acts 10:1-3] as Cornelius was already a God fearing man. Peter was sent by the Holy Spirit to show a way for the Gentiles because God's chosen Apostle Paul was yet in Arabia sorting things out [Galatians 1:17].
Peter was never in Rome! I realize this statement destroys much of Catholicism's tradition.....but "C'est la vie"!