Five + adjective + noun — what case is adj in?

Question

I have a construction

... пят(-ь/-и/-ю) [adjective] [noun]

I want to know which case the adjective should be in when the noun/number are in nominative, accusative, or oblique cases.

I know the rules for 2, 3, and 4 as listed out here:

While the noun in a nominative construction is in the genitive singular following два or две, an intervening adjective or adjectival participle will be in the genitive plural or nominative plural

If два is in nominative case, the adjective will be nominative plural when the noun is feminine

If два is in accusative case, the adjective will be nominative plural only if the noun is feminine inanimate

but what are the rules for 5, 13, 22, etc.?

Answer 1

5 and more need Genitive plural:

5 or 13 кошек / собак / бегемотов / слонов.

But if it is a number more than 20 and it ends in 1, 2, 3, or 4, then the rules for 1, 2, 3, or 4 apply:

21 кошка / собака / бегемот / слон

22 or 23 or 24 кошки / собаки / бегемота / слона

Do not forget that 1 and all other numbers more than 20 ending in 1 agree in gender with the items being counted, for masculine it is один, for feminine одна, and for neuter одно. 2 and numbers more than 20 ending in 2 have only two gender forms, два for masculine and neuter, две for feminine.

If you put the whole expression Numeral+Noun into a case other than Nominative, then both the numeral and the noun are in the case you needed, the noun will be in plural if the numeral is not 1 or more than 20 ending in 1, in this case the noun is singular.

Dative Case as an examle:

Пяти or тринадцати or двадцати двум кошкам / собакам / бегемотам / слонам.

двадцати одной кошке / собаке / двадцати одному бегемоту / слону

Answer 2

These rules regarding cases and numbers are mind-numbing. The best way to assimilate these rules is to examine a large volume of sentences and texts so you can see how the rules are applied in context. You'll catch onto it soon enough. I subscribe to Learnwitholiver.com. There are probably other similar online resources, but I'm not aware of those.