The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
11. (The assertion that there is scriptural authority for the pradhâna, &c. can) also not (be based) on the mention of the number (of the Sânkhya categories), on account of the diversity (of the categories) and on account of the excess (over the number of those categories).
The attempt to base the Sânkhya doctrine on the mantra speaking of the agâ having failed, the Sânkhya again comes forward and points to another mantra: 'He in whom the five "five-people" and the ether rest, him alone I believe to be the Self; I who know believe him to be Brahman' (Bri. Up. IV, 4, 17). In this mantra we have one word which expresses the number five, viz. the five-people, and then another word, viz. five, which qualifies the former; these two words together therefore convey the idea of five pentads, i.e. twenty-five. Now as many beings as the number twenty-five presupposes, just so many categories the Sânkhya system counts. Cp. Sânkhya Kârikâ, 3: 'The fundamental causal substance (i.e. the pradhâna) is not an effect. Seven (substances), viz. the Great one (Intellect), and so on, are causal substances as well as effects. Sixteen are effects. The soul is neither a causal substance nor an effect.'
[paragraph continues] As therefore the number twenty-five, which occurs in the scriptural passage quoted, clearly refers to the twenty-five categories taught in the Sânkhya-smriti, it follows that the doctrine of the pradhâna, &c. rests on a scriptural basis.
To this reasoning we make the following reply.--It is impossible to base the assertion that the pradhâna, &c. have Scripture in their favour on the reference to their number which you pretend to find in the text, 'on account of the diversity of the Sânkhya categories.' The Sânkhya categories, have each their individual difference, and there are no attributes belonging in common to each pentad on account of which the number twenty-five could be divided into five times five. For a number of individually separate things can, in general, not be combined into smaller groups of two or three, &c. unless there be a special reason for such combination.--Here the Sânkhya will perhaps rejoin that the expression five (times) five is used only to denote the number twenty-five which has five pentads for its constituent parts; just as the poem says, 'five years and seven Indra did not rain,' meaning only that there was no rain for twelve years.--But this explanation also is not tenable. In the first place, it is liable to the objection that it has recourse to indirect indication. 1 In the second place, the second 'five' constitutes a compound with the word 'people,' the Brâhmana-accent showing that the two form one word only. 2 To the same conclusion we are led by another passage also (Taitt. Samh. I, 6, 2, 2, pañkânâm tvâ pañkaganânâm, &c.) where the two terms constitute one word, have one accent and one case-termination.
[paragraph continues] The word thus being a compound there is neither a repetition of the word 'five,' involving two pentads, nor does the one five qualify the other, as the mere secondary member of a compound cannot be qualified by another word.--But as the people are already denoted to be five by the compound 'five-people,' the effect of the other 'five' qualifying the compound will be that we understand twenty-five people to be meant; just as the expression 'five five-bundles' (pañka pañkapûlyah) conveys the idea of twenty-five bundles.--The instance is not an analogous one, we reply. The word 'pañkapûli' denotes a unity (i.e. one bundle made up of five bundles) and hence when the question arises, 'How many such bundles are there?' it can be qualified by the word 'five,' indicating that there are five such bundles. The word pañkaganâh, on the other hand, conveys at once the idea of distinction (i.e. of five distinct things), so that there is no room at all for a further desire to know how many people there are, and hence no room for a further qualification. And if the word 'five' be taken as a qualifying word it can only qualify the numeral five (in five-people); the objection against which assumption has already been stated.--For all these reasons the expression the five five-people cannot denote the twenty-five categories of the Sânkhyas.--This is further not possible 'on account of the excess.' For on the Sânkhya interpretation there would be an excess over the number twenty-five, owing to the circumstance of the ether and the Self being mentioned separately. The Self is spoken of as the abode in which the five five-people rest, the clause 'Him I believe to be the Self' being connected with the 'in whom' of the antecedent clause. Now the Self is the intelligent soul of the Sânkhyas which is already included in the twenty-five categories, and which therefore, on their interpretation of the passage, would here be mentioned once as constituting the abode and once as what rests in the abode! If, on the other hand, the soul were supposed not to be compiled in the twenty-five categories, the Sânkhya would thereby abandon his own doctrine of the categories being twenty-five. The same
remarks apply to the separate mention made of the ether.--How, finally, can the mere circumstance of a certain number being referred to in the sacred text justify the assumption that what is meant are the twenty-five Sânkhya categories of which Scripture speaks in no other place? especially if we consider that the word gana has not the settled meaning of category, and that the number may be satisfactorily accounted for on another interpretation of the passage.
How, then, the Sânkhya will ask, do you interpret the phrase 'the five five-people?'--On the ground, we reply, of the rule Pânini II, 1, 50, according to which certain compounds formed with numerals are mere names. The word pañkaganâh thus is not meant to convey the idea of the number five, but merely to denote certain classes of beings. Hence the question may present itself, How many such classes are there? and to this question an answer is given by the added numeral 'five.' There are certain classes of beings called five-people, and these classes are five. Analogously we may speak of the seven seven-rishis, where again the compound denotes a class of beings merely, not their number.--Who then are those five-people?--To this question the next Sûtra replies.
258:1 Indication (lakshanâ, which consists in this case in five times five being used instead of twenty-five) is considered as an objectionable mode of expression, and therefore to be assumed in interpretation only where a term can in no way be shown to have a direct meaning.
258:2 That pañkaganâh is only one word appears from its having only one accent, viz. the udâtta on the last syllable, which udâtta becomes anudâtta according to the rules laid down in the Bhâshika Sûtra for the accentuation of the Satapatha-brâhmana.