The following graph attempts to illustrate the meaning of "the many" in Romans Chapter 5. Please note the yellow highlighted areas, which correspond to the four instances where the phrase "the many" occurs in Romans 5 (NASB translation). Please note how the Apostle Paul juxtaposes Adam with Christ Jesus, and flip-flops the causes-and-effects of obedience versus disobedience.
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In Romans 5, the Apostle Paul juxtaposes Adam with Christ Jesus, and flip-flops the causes-and-effects of obedience versus disobedience. That is, the first Adam disobeyed God in the Garden of Eden, while the second Adam later obeyed God in the Garden of Gethsemane (i.e., Jesus had said, "not my will, but your will be done," and so rather than let the cup pass from him, he had accepted the will of his father).
In this regard, the disobedient first Adam had already catapulted the entire human race into spiritual separation from God through his disobedience. All human beings ("the many") are thus born into the state of spiritual death (top left-hand box in the graph). This spiritual death made "the many" to be sinners or transgressors against God (bottom left-hand box in the graph). That is, all human beings commit transgressions as individual acts of disobedience.
Before continuing, one note is necessary -- the key difference between both figures here was that the one man (first Adam) was a living soul (1 Cor 15:45) and the other man (second Adam) was a life-giving spirit, who existed as eternal life (1 Cor 15:45). This difference helps to understand how each man, respectively, affects "the many."
For example, the second Adam comes into the world and dies for the sins of the entire world. He dies for the sins of the entire world because he is not under the curse of spiritual death, and so he had never sinned (2 Cor 5:21). As the second Adam he absorbs the transgressions of the entire world in his own body (2 Cor 5:21). So as the second Adam, he tastes death "for all men," since he dies for the sins of the entire world (1 Jn 2:2). Thus grace abounded to "the many" (top right-hand box in the graph).
In this respect, then, those who believe in Jesus Christ are not only forgiven of their sins, but they are "born again," because while they once were dead spiritually (as unbelievers), they are now made alive anew with eternal life (Jn 3:5-7). That is, the sinner receives righteousness through faith, which results in the free gift of eternal life -- thus "the many" are made righteous (please see the bottom right-hand box in the graph). This does not mean that believers become sinless people, but that they do not "practice" unrighteousness (1 Jn 2:29; 1 Jn 3:10; Rev 22:11; inter alia). As biological descendants of the first Adam, believers still exist in bodies descended from the first Adam while on this earth.
Again, the sins of the ENTIRE world were condemned and nailed to the cross (Col 2:14). In another place, the Apostle Paul wrote that Christ Jesus gave Himself as a ransom "for all" (1 Tim 2:6). Another passage indicates that the desire of "God our Savior" is that "all men" be saved (1 Tim 2:4 and 2 Pet 3:9). The Apostle John says that Christ Jesus died "for the sins of the whole world, and not just for the sins of believers" (paraphrase of 1 Jn 2:2). Finally, the writer of the Book of Hebrews indicates that Christ Jesus tasted death "for everyone" (Heb 2:9). These passages indicate that all peoples are eligible to hear the good news of the gospel message because their sins were atoned for at the cross. If they do not receive the free gift of eternal life available through the gospel message, however, they will not have the righteousness to escape the last judgment.
Thus the "justification of life" to "the many" (please see top right-hand box) means that all human beings are promised resurrection. In this regard, at the last judgment it is not the "books of sins" that are not opened, but the "books of (dead) works." In other words, sins are not the basis of the indictment at the last judgment, but the spiritual death, which was the source of dead works, which includes self-righteousness -- that is, without righteousness and eternal life through Jesus Christ, the Lake of Fire is the destiny of the unsaved, whose names are not found in the Book of Life (Rev 20:14). The reason this judgment is called "the second death" is because these persons receive resurrected bodies (because their sins were atoned at the cross). However, what lacks at the last judgment is their eternal life, which would have come through righteousness by faith. Thus these persons suffer "the second death" when thrown into the eternal Lake of Fire forever.