So, let's look at the few verses preceding 1 John 5:3.
1Jo 4:20 If a man say, I love God, and hates his brother, he is a liar: for he that loves not his brother whom he has seen, how can he love God whom he has not seen?
1Jo 4:21 And
THIS COMMANDMENT have we from him,
so that (hina: with the intention that)
he who loves God should love his brother also.
1Jo 5:1 Whosoever is believing
that (hoti) Jesus is the Christ is born of God:
and every one loving him having begat loves him also having been begotten of him.
1Jo 5:2 In
this we know
that (hoti) we are loving the children of God whenever (hotan) we are loving God, and are keeping his commandments.
1Jo 5:3 For
this is the love of God,
so that (hina: with the intention that) we may keep on keeping his commandments: and his commandments are not grievous.
In 1 John 4:21, to what COMMANDMENT is John referring as "this commandment" ? I believe it is the commandment to love one another: the commandment that is woven into and throughout the fabric of 1 John.
1Jo 2:7 Brethren, I write
no new commandment unto you, but
an old commandment which ye had from the beginning. The old commandment is the word which ye have heard from the beginning.
1Jo 2:8 Again,
a new commandment I write unto you, which thing is true in him and in you: because the darkness is past, and the true light now shineth.
1Jo 2:9 He that saith he is in the light, and hateth his brother, is in darkness even until now.
1Jo 2:10 He that loveth his brother abideth in the light, and there is none occasion of stumbling in him.
1Jo 3:10 In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God,
neither he that loveth not his brother.
1Jo 3:11 For this is the message that ye heard from the beginning, that we should love one another.
1Jo 3:14 We know that we have passed from death unto life,
because we love the brethren. He that loveth not
his brother abideth in death.
1Jo 3:16 Hereby perceive we the love
of God, because he laid down his life for us: and
we ought to lay down our lives for the brethren.
1Jo 3:18 My little children,
let us not love in word, neither in tongue; but in deed and in truth.
1Jo 4:7 Beloved, let us love one another: for love is of God; and every one that loves is born of God, and knows God.
1Jo 4:11 Beloved, if God so loved us,
we ought also to love one another.
1Jo 4:16 And we have known and believed the love that God has to us. God is love; and
he that dwell in love dwells in God, and God in him.
1Jo 4:20 If a man say, I love God, and hates his brother, he is a liar: for he that loves not his brother whom he has seen, how can he love God whom he has not seen?
1Jo 4:21 And this commandment have we from him,
so that (hina: with the intention that)
he who loves God should love his brother also.
1Jo 5:1 Whosoever is believing
that (hoti) Jesus is the Christ is born of God:
and every one loving him having begat loves him also having been begotten of him.
So, why does John say
1Jo 4:21 And
THIS COMMANDMENT have we from him,
so that (hina: with the intention that)
he who loves God should love his brother also.
If God had not commanded us to love one another, we would feel justified in reactively mistreating our brothers and sisters even though we were convinced that we love God. That is why John says :We have this commandment so that we who love God will also in practice, in deed and truth, love our brother and sister.
Now, moving on to 1 John 5:1-3,.
1Jo 5:1 Whosoever is believing
that (hoti) Jesus is the Christ is born of God:
and every one loving him having begat loves him also having been begotten of him.
In 5:1, John affirms that the way we are regenerated is by believing in Jesus. And he also affirms that the person who is truly loving God genuinely values those who are God's children, It would offend God for us to devalue His children. And if we love God, we don't want to offend Him.
v. 2 In
[loving God and keeping His commandments] we know
that (hoti) we are loving the children of God, whenever we are loving God and keeping His commandments.
In 5:2, John is telling us that when we are showing our love for God by treating our brothers and sisters according to God's commandments, we are truly loving God's children.
1Jo 5:3 For
this [loving both God and the children of God] is the love of God,
so that (hina: with the result that) we may keep on keeping his commandments: and his commandments are not grievous.
In 5:3 John tells us that the love of God is not just loving God, but loving both God and the children of God. And He tells us that we are commanded to love
both God and the children of God in order that we may enthusiastically obey God and not find doing so difficult and depressing. To be obeying God out of a genuine love for Him and His people is far easier and more rewarding than obeying God out of fear of retribution or out of mere duty.
So, I would say that reading hina in 1 John 5:3 as "so that/with the result that or in order that/with the intention that" makes perfect sense, at least to me.