Romans 13:3-5 meaning

The government's assigned purpose is to punish evil, and reward good. There is no real reason for us to fear our government if we obey the law, for rulers are not a cause of fear for good behavior, but for evil (v 3). The government has been established by God, and it has the power to impose the law by force (the sword). God's purpose for the government is to resist violence and bring about peace. 

Do you want to have no fear of authority? Do what is good and you will have praise from the same; for it is a minister of God to you for good (vv 3-4). We won't have reason to fear the government if we don't break the law. Earlier in Romans 12:19, Paul writes that vengeance is God's business, and His wrath will pour out on evildoers. 

Likewise, the government makes laws to punish lawbreakers, and whether it realizes it or not, it does this under God's allowance. So if you do what is evil be afraid; for it [the government] does not bear the sword for nothing (v 4). The phrase bear the sword means that God has given moral authority to government to use coercive force in order to do good and deter evil. 

At the time of this letter, Rome is a polytheistic pagan society, so the Roman rulers certainly do not believe in the one true God (as far as we know); even so, their authority is appointed by God. It is a surrogate for God's wrath against wickedness. God claims ownership of vengeance (Romans 12:19), and in this passage Paul writes that the government is a minister of God, an avenger who brings wrath on the one who practices evil (v 4). God has delegated justice to ruling authorities. In the United States God has appointed the citizens to have the ultimate human sovereignty over government because our constitution vests the ultimate power in "We the People." Therefore, it is our responsibility to do our part to see that the government does good and punishes evil, rather than the other way around. 

So, believers in Jesus have a particular obligation to be good stewards of their citizenship, as the Spirit leads. Citizens can participate directly as well as organize with other citizens and have substantial influence on government. God authorizes earthly authority, and He also holds earthly authority accountable. Everyone has a different role to play, but followers of Jesus who do not exercise their citizenship as unto the Lord will have to answer to God in the same way a ruler will have to answer to God.

In light of the relationship of God to government, and government to the individual citizen, it is necessary to be in subjection to the laws not only to avoid the penalty of the law (because of wrath), but also for conscience' sake (v 5). We are in accordance with God's design by submitting to the law.

Verse 4 says the sword was given to the government to minister to us for good. That means the government has moral authority to use violence in order to enforce the law. This was instituted by God in Genesis 9:6, when God granted the authority to man to take the life of man in order to prevent the earth from filling with violence again. God destroyed the earth with water because it had filled with violence (Genesis 6:11). He gave moral authority to human government to take life in order to deter violence from spreading. 

At the end of this chapter, Paul encourages laying aside deeds of darkness and behaving properly, to be ready for when Jesus comes back (vv 12, 13). Obeying our country's laws is a part of behaving properly; being decent, respectable citizens for our own personal readiness to join Christ at His return. 

None of Paul's writing discounts the fact that sometimes the government acts wrongly or convicts the wrong person. When this occurs, we should contest it; Paul appealed to Caesar when he was not getting justice at a lower level (Acts 25:11). He used the legal system appropriately to fight for his life. 

There are instances in the Bible where Christians appropriately break laws because the laws directly contradict God's commands, such as when the Apostles refuse to stop speaking the name of Jesus when ordered to do so (Acts 4:18-20). And there are times when authorities conflict, and it is our job to obey the higher authority. But this passage makes it clear that our responsibility is to seek for ways to follow rather than avoid the law.