John Gill Commentary 1 Chronicles 5

Now the sons of Reuben, the firstborn of Israel
Are as follow in (1 Chronicles 5:3) where the account begins; for what comes between this and that is in a parenthesis:

for he was the firstborn ;
of Jacob by his wife Leah; that must be owned, and Jacob allows it, (Genesis 49:3) and yet the genealogy in this book begins not with him, as might on that account be expected; the reason follows:

but forasmuch as he defiled his father's bed :
by lying with Bilhah his concubine:

his birthright was given unto the sons of Joseph the son of Israel ;
his beloved son by his beloved wife Rachel and so had a double portion given him; his two sons being equally ranked with the other sons of Jacob, and became distinct tribes, and each had their lot in the land of Canaan, see (Genesis 48:5Genesis 48:22) compared with (Deuteronomy 21:17)

and the genealogy is not to be reckoned after the birthright ;
or, "but the genealogy" ^F15 ; neither after the birthright of Reuben, which he had by nature, being Jacob's firstborn; nor after the birthright of Joseph, which be had by his father's gift, as it might be thought it should; the reason of which follows.

FOOTNOTES:

• F15: "Nee tamen", Tigurine version.

For Judah prevailed above his brethren
That is, the tribe of Judah prevailed above the rest in number, in valour, and courage, and in dignity; therefore the genealogy is not reckoned according to birthright, but dignity and dominion; hence this genealogical account began with Judah,

[because] of him [came] the chief ruler ;
David and the kings of Judah, his successors; and above all, from him the Prince Messiah was to spring, and did, according to (Genesis 49:10) so both the Syriac and Arabic versions read, ``out of Judah should go forth the King Messiah:'' but the birthright [was] Joseph's
or "though" ^F16 it was; yet Judah having the dominion and dignity, that tribe is first genealogized.

FOOTNOTES:

• F16: Licet, ibid. (Tigurine version)

The sons, [I say], of Reuben the firstborn of Israel, were,
Hanoch, and Pallu, Hezron, and Carmi .
] As in (Genesis 46:9) .

Who was either the son of Carmi last mentioned, or rather of Hanoch, Reuben's firstborn, since the descendants of him were the princes of the tribe: his posterity in succession were, Shemaiah, Cog, Shimei, Micah, Reaia, Baal, Beerah; of whom we know no more than their names, and by these the descent is carried down to the captivity by Tiglathpileser, as follows.

(See Gill on 1 Chronicles 5:4).