1 John 5:1-5

1 Whoever believes that Jesus is the Christ is born of God, and everyone who loves Him who begot also loves him who is begotten of Him.

² By this we know that we love the children of God, when we love God and keep His commandments.

³ For this is the love of God, that we keep His commandments. And His commandments are not burdensome.

⁴ For whatever is born of God overcomes the world. And this is the victory that has overcome the world—our faith.

⁵ Who is he who overcomes the world, but he who believes that Jesus is the Son of God?

whoever (v.1) = lit. “everyone that believes,” “every  believer”

is born of God (v.1) = “has been born”

Since every believer has part in the gift of Divine life, by which he is born of God, it is inevitable that this life will be manifested in love to those who likewise are born of God (v.1) … The whole of this passage teaches, not that in loving our brother we rise to the love of God, but that, on the contrary, God Himself is the source of all the love that we can and do show.— Vine, page 93.

By this we know (v.2) = lit. “By this we have the constant experience of knowing”

In [1 John 4:20-21] love to God is the fulfilment of His commandments, which are shown to have their evidence in the love of His children. This same truth is stressed by being put in the converse way in the present passage (v.2). In other words, if we want to know whether we love our brother, it is necessary to ask if we love God, for the motive cause of love lies in God Himself, for “God is love.” Here the test of our love to God is the doing of His commandments, that is to say, in loving our neighbor. Taken together, then, the two passages show that love to God and love to one another are essentially associated and mutually evidential. — Vine, page 94.

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commandments (v.3) — [God’s] commandments make known His nature, and we show His nature when we keep them. — Vine, page 94.

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burdensome (v.3) — The statement does not mean this, that God’s commandments are not difficult to keep, it means that they do not impose a burden when they are kept (Psalm 19:11; Matthew 11:30). … the Lord supplies strength for the fulfilment of His commandments, His love makes them light, and He rewards the doing of it. — Vine, pages 94-95.

Yet again, remember John was writing to believers of the kingdom gospel who had/will have the law written on their hearts. So, to hate a brother proved that the Spirit hadn’t written the law on their hearts, which, in turn, proved that they didn’t believe in Jesus Christ. Or to put it another way:

A genuine begotten one will love a fellow begotten one because of the work of the Spirit. Why then the command to love (1 John 4:21). Because, for the kingdom believer, the command to love works in harmony with the Spirit of God and their will, to cause them to obey God’s Word. The command to love will also reveal the hearts of the people making a profession of knowing God. For the believer, loving each other will reveal that they have the Spirit of God and are born of God; for the false professor the lack of love (or hating their brother) will prove that they lack eternal life. — Grace, page 2224.

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The spirit of the world is opposed to the fulfilment of the commandments of God. To do His commandments, therefore, is to overcome (v.4) the spirit of the world. — Vine, page 95.

overcome (v.4) = conquer, defeat, prevail

Faith (v.4) not merely brings to us the new birth, but with it the power to overcome the opposition of the spirit that characterizes the world. The victory which was thus gained by faith, the proving of things not seen, brought us into a life which was designed to be characterized by victorious power. — Vine, page 95.