John Gill Commentary Daniel 11:5

"And the king of the south shall be strong, and [one] of his princes; and he shall be strong above him, and have dominion; his dominion shall be a great dominion." — Daniel 11:5 (ASV)

And the king of the south shall be strong
That is, the king of Egypt, which lay south to Syria, as Syria lay north to Egypt; and therefore the king of the one is called the king of the south, and the other the king of the north, throughout this prophecy; and by the king of the south, or Egypt, is here meant Ptolemy Lagus, one of Alexander's generals, who had Egypt for his share; and a very powerful king he was; for he reigned over Egypt, Lybia, Cyrene, Ethiopia, Arabia, Phoenicia, Coelesyria, Cyprus, and several isles in the Aegean sea, and many cities in Greece:

and one of his princes ;
not of Ptolemy king of Egypt, but of Alexander the great; and this is Seleucus Nicator, afterwards called king of the north, having Syria for his part, which lay to the north of Egypt, as before observed: and he shall be strong above him, and have dominion ;
that is, be a greater and more powerful prince than Ptolemy king of Egypt: his dominion shall be a great dominion ;
even greater than the others; for he reigned over Macedonia, Greece, Thrace, Asia, Syria, Babylonia, Media, and all the eastern countries as far as India; even from Taurus to the river Indus, and so likewise from Taurus to the Aegean sea:

these two are only mentioned, who shared the Persian monarchy, because the Jews were only affected by them, for the sake of whom this prophecy is delivered.