What about a slightly different view?
Heb 5:12 In fact, though by now you should be teachers, you still need someone to teach you the basic truths of God's word. You have become people who need milk instead of solid food food. Heb 5:13 For everyone who lives on milk is still a baby and is inexperienced in the message of righteousness.
Two things are in view Righteousness and understanding Gods word and applying it to your life.
Lets look at another verse to se what is being spoken of:
II Tim: [16] All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: [17] That the man of God may be perfect, thoroughly furnished unto all good works.
So it is the word of God that needs to be understood and acted upon to bring us to righteousness. And what is the result of this? We do good works. Good works are our righteous deeds. What we call Mitvah.
So what is the word of God here? The New Testament? Nope! Was no such thing when this was written. The reference is to the Jewish Bible, or what you call the old testament. It is Torah, the prophets and the writings. We call it the Tanakh. This is where we come to maturity, through studying and applying Gods word, specifically Torah, and the rest of the old testament so that we can Establish doctrine, for reproof and correction and training up in righteousness. You might suprised by this but the word righteous means, "to be obedient to divine law, obeying the commandments of God". The New testament epistles are all about the young church learning to use the old testament and growing in maturity and applying the principles and laws of God to their lives.
I John says 2: [3] And hereby we do know that we know him, if we keep his commandments. [4] He that saith, I know him, and keepeth not his commandments, is a liar, and the truth is not in him.