First off, in two of the five times that it is used, it is not used of God, but of men, and surely men do not have an omniscience that requires foreknowledge. In fact, in those two instances, the word _proginosko_ is used to say that men knew something before, in times past.
One occurrence of the word, when used in reference to men is:
Acts 26:5 They have known me for a long time (_proginosko_) and can testify, if they are willing, that according to the strictest sect of our religion, I lived as a Pharisee. (NIV) Acts 26:5 Which knew me from the beginning (_proginosko_), if they would testify, that after the most straitest sect of our religion I lived a Pharisee. (KJV)
Who had _proginosko, in Acts 26:5? Who had “foreknowledge?’ The answer is in v.4: Acts 26:4 The Jews all know the way I have lived ever since I was a child, from the beginning of my life in my own country, and also in Jerusalem.
Paul is presenting his defense to Agrippa, and says that the Jews KNEW HIM BEFORE (proginosko). The use of the word, _proginosko_, does not, in this instance, require, divine foreknowledge or omniscience. Paul is merely saying that his accusers KNEW BEFORE what his life had been like.
The second occurrence of the word _proginosko_, when used in reference to men occurs in:
2 Pet. 3:17 Therefore, dear friends, since you already know (_proginosko_) this, be on your guard so that you may not be carried away by the error of lawless men and fall from your secure position. (NIV) 2 Pet. 3:17 Ye therefore, beloved, seeing ye know these things before, (_proginosko_) beware lest ye also, being led away with the error of the wicked, fall from your own steadfastness. (KJV)
Who had _proginosko_, “foreknowledge,” in 2 Pet 3:17? The answer is found in the opening salutation of the book. Peter addresses his letter: 2 Pet. 1:1 Simon Peter, a servant and apostle of Jesus Christ, To those who through the righteousness of our God and Savior Jesus Christ have received a faith as precious as ours:
The Christians who received Peter’s letter are the one who KNEW these things BEFORE. Again, no divine foreknowledge of events beforehand is required. Men are not omniscient, so this usage of the word _proginosko_ cannot mean “foreknowledge” in the sense that most people mean when they use it. They just KNEW the things that Peter is writing about BEFORE, and he is just reminding them of these things.
No “foreknowledge” is required here.