Rom 5:13,14 for before the law was given, sin (the sinful nature) was in the world. But sin is not taken into account when there is no law. Nevertheless, (spiritual) death reigned from the time of Adam to the time of Moses, even over those who did not sin by breaking a command, as did Adam, who was a pattern of the one to come
I take this first of all to mean simply that the sinful nature was not introduced by the law, but rather the sinful nature is part of human nature, and thus precedes the law. The reason why he might be bringing up that fact is to say that the law is not the problem. Throughout history and today there are people who think they can solve the problem of sin in the world through legislation. But if history teaches us anything, it teaches us that sin is much more ingrained and cannot be done away with through legal regulations.
True, if there were no laws, people could not be reckoned guilty, even though complying with their sinful nature. For there would be nothing they were transgressing against. But again remember what Paul had already pointed out. "(Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law, since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.)" Rom 2:14,15 Thus we find whole societies generally agreeing upon what is right and wrong, because human nature also has a conscience, to which each of us will be held accountable.
Therefore even prior to written law, people became spiritually dead because they did what they knew was wrong, in compliance with their sinful nature, or failed to do what was right. Adam had law. He explicitly knew God's command. But it doesn't take explicit commandments to know right from wrong. And thus all are guilty who comply with the desires of their sinful nature.