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When a noun is followed by a number (a numbered noun) do we need an article before it?
e.g. page 5 vs the page 5.
What is the grammatical term for such groups?
I read about other types of numerical structures here https://www.ucl.ac.uk/internet-grammar/determin/numerals.htm but this case was not covered.
The grammar here seems odd. The number has "cardinal" form (one, two, three) but it is answering the question "which page", and so is functioning like an ordinal (first, second, third). It also follows the noun, instead of preceding it, as a determiner would. On the other hand, "page" can't be a determiner of a noun "five", as determiners are a closed class.
Instead you should understand the phrase "page 5" to function as a name. And the number is acting as a proper noun to identify the page. As such it is similar to "Captain Smith" or "The Starship Enterprise". The word "page" mentions the type of object and 5 identifies which page. Note that "page 5" may not be the fifth page! Many books have frontmatter that is numbered "i, ii, iii", so "page 1" is not the first physical page in the book.
Similarly, in a recent race, I was "runner 1604", that doesn't mean I was the one thousand and sixty fourth runner (only about 300 of us were running) but I am the fourth runner in club sixteen. Likewise "room 1206" in a hotel doesn't mean that there are 1205 other rooms.
So if we treat "page 5" as a proper noun (even though it isn't capitalised as one) then we use "the" only if the word "the" is part of the name. In this context "the" isn't part of the name.
At the end of all that grammar, I come to the conclusion: You say "page 5", not "the page 5".
On the other hand, with a real ordinal, you would say "the fifth page".
See also https://english.stackexchange.com/questions/250568/on-page-seven-vs-on-a-the-page-seven
I cannot think of a case offhand where "the page 5" would be correct. It's just "page 5".
