Where does the ending –ек come from after numbers?
I just learned that after numbers 5 and up, the noun should be in the genitive plural. However, the example sentences in the software I'm learning from include phrases like шесть девочек and десять кошек (other nouns seem to take this ending too; those were just examples).

This –ек ending for feminine nouns doesn't appear in any grammar table I've seen for the genitive plural and I can't find any websites mentioning it as an irregular declension.

Can anyone explain why these nouns don't take the regular endings in this situation?

Question

Where does the ending –ек come from after numbers?
I just learned that after numbers 5 and up, the noun should be in the genitive plural. However, the example sentences in the software I'm learning from include phrases like шесть девочек and десять кошек (other nouns seem to take this ending too; those were just examples).

This –ек ending for feminine nouns doesn't appear in any grammar table I've seen for the genitive plural and I can't find any websites mentioning it as an irregular declension.

Can anyone explain why these nouns don't take the regular endings in this situation?

Answer

If your principal question is "why", this phenomenon has historical reasons. Some centures ago, the "-ка" followed "ъ" or "ь". That time the letters "ъ" and "ь" were not just an orthographic feature. They specified very short vowels, which usually disappeared or became "о" and "е" respectively (depending on their position in the word):

ложька (Nom. Sing.) => ложка
ложькъ (Gen. Plur.) => ложек

палъка (Nom. Sing.) => палка
палъкъ (Gen. Plur.) => палок

Answer

Hello! 
When the noun ends in “consonant + ка”, in the genitive plural we replace the “ка” with “ок” or “ек”, depending on the preceding consonant:

1. AFTER Ж, Ш, Щ and Ч “ЕК” IS USED:
ло́жка => пять ло́жЕК
де́вушка => пять де́вушЕК
де́вочка => пять де́вочЕК

2. AFTER OTHER CONSONANTS WE ADD “ОК”:
буты́лка => пять буты́лОК
ма́рка => пять ма́рОК

3. “Ь” AND “Й” DISAPPEAR AND THE “ЕК” IS ADDED: 
сосу́лька => пять сосу́лЕК
ма́йка => пять ма́ЕК

Answer

But the thing that you've discovered is totally regular:)
-ка ALWAYS has a 'mobile' vowel before it:)

Answer

I can only confirm Yevgeni's answer:)

Grammar tables don't include it because it is stem alteration, not different endings.

These changes are so irregular and so much related to particular root, that Complete paradigm (treating diffrent stress patterns as different declension types) would be scary - some dozens of noun declension types:/ 
I can find a complete list for you if you want:)))

Answer

There are many different endings in the genitive plural

Склонение	                       Примеры
1 склонение                	Сосен_, тарелок_, черешен_, земель_, мужчин_, дедушЕК_

2 склонение	                СлонОВ, столбОВ, королЕЙ, гениЕВ, блюд_, зёрен_, платьЕВ, устьеЕВ, селенИЙ, решенИЙ

3 склонение         	МетелЕЙ, ночЕЙ, дочерЕЙ

Разносклоняемые     ПутЕЙ, детЕЙ, времен_, знамён_
существительные

Существительные,     Ножниц_, каникул_, штанОВ, очкОВ, дрожжЕЙ, буднЕЙ
которые имеют 
только формы
 мн. числа