Jamieson, Fausset and Brown on Jeremiah 23:5

5. As Messianic prophecy extended over many years in which many political changes took place in harmony with these, it displayed its riches by a variety more effective than if it had been manifested all at once. As the moral condition of the Jews required in each instance, so Messiah was exhibited in a corresponding phase, thus becoming more and more the soul of the nation's life: so that He is represented as the antitypical Israel (Is 49:3).

unto David--Hengstenberg observes that Isaiah dwells more on His prophetical and priestly office, which had already been partly set forth (De 18:18; Psa 110:4). Other prophets dwell more on His kingly office. Therefore here He is associated with "David" the king: but in Is 11:1 with the then poor and unknown "Jesse."

righteous Branch--"the Branch of righteousness" (Jr 33:15); "The Branch" simply (Zec 3:8; 6:12); "The Branch of the Lord" (Is 4:2).

prosper--the very term applied to Messiah's undertaking (Is 52:13, Margin; Is 53:10). Righteousness or justice is the characteristic of Messiah elsewhere, too, in connection with our salvation or justification (Is 53:11; Da 9:24; Zec 9:9). So in the New Testament He is not merely "righteous" Himself, but "righteousness to us" (1Co 1:30), so that we become "the righteousness of God in Him" (Ro 10:3, 4; 2Co 5:19-21; Php 3:9).

execute judgment and justice in the earth--(Psa 72:2; Is 9:7; 32:1, 18). Not merely a spiritual reign in the sense in which He is "our righteousness," but a righteous reign "in the earth" (Jr 3:17, 18). In some passages He is said to come to judge, in others to reign. In Mt 25:34, He is called "the King." Psa 9:7 unites them. Compare Da 7:22, 26, 27.