The law, says Paul, was 'weak through the flesh' :
For what the law could not do, in that it was weak through the flesh ... [Romans 8:3 KJV].
That is to say the law would work, in and of itself, but the medium through which it would work - the flesh - was weak. This weakness, of flesh, cannot sustain the working of law. It fails.
'I am carnal' says Paul. 'What I would, that do I not' ... 'but what I hate, that do I', Romans 7:15.
Paul knows what to do : 'I delight in the law of God, after the inward man'. He not only agrees with it, he delights in it.
But he does not do it.
Because he is weak.
The weakness is due to pathema, παθημα. 'Affliction' or 'suffering' is the way the word is elsewhere translated. It is the passive state of weakness common to flesh.
Flesh and blood are not strong, they are subject to all kinds of distress, calamity, inherent weakness, tragedy, infection, contagion and death itself.
Mankind was never created to be strong, in and of itself. The Creator did not leave mankind to fend for itself : he provided in every possible way and he warned that there was a way of attempting to live that was not viable.
It would end in death. The tree of knowledge cannot sustain life, it cannot be digested, it is toxic and death will result.
In the inception of humanity, humanity was warned, 'Thou dost not eat of it.' It isn't food. You cannot assimilate it (as a source of life). You will kill yourself.
For flesh is weak. And the law cannot work through flesh.
Because of pathema.
Pathemata, παθηματα (Romans 7:5) is the nominative plural, expressing that there is a whole variety of weaknesses in flesh that render it incapable of accomplishing the task of keeping the law in its every word, every dictate, every requirement : every word, every sentence, every commandment, day by day, moment by moment, decade by decade.
The 'motions of the sins' (there are two articles present) should be translated 'the weaknesses of the sins' in my view : being the cause of the sins in the first place. I can see why 'motions' is used (in the KJV or 'passions' by Young) but it is not clear enough.
The origin of the sins is not the law. That origin is the weakness of flesh which, attempting to keep law, fails and results in sins.
The flesh should never have attempted to live that way.
And this failure was expressed 'through', δια, dia, the law, the concept conveying the law to be a medium not an agency. Agency would be expressed as a dative case, perhaps, or another preposition ; απο, apo, for example.
There could be no success, attempting to express law through the medium of flesh.
It was destined to failure.
But there is another way : the Tree of Life.
For the rule of the Spirit (of Life in Christ Jesus) hath made me free from the rule of sin and death. [Romans 8:2.]
[Greek literal (TR - Stephanus) with my own brackets and translating νομοσ in its broadest sense.]