Bækurnar eru fimm alls.

Because bækurnar means the books.

In Icelandic, the definite article is usually added to the end of the noun instead of being a separate word like English the.

• bók = book
• bækur = books
• bækurnar = the books

So the ending -nar here is the definite ending for this plural form.

Also note that bók changes to bækur in the plural, so this is not just bók + something. It is an irregular plural pattern you simply have to learn.

Because the subject is plural.

• er = is (singular)
• eru = are (plural)

Since bækurnar means the books, the verb must also be plural:

• Bókin er... = The book is...
• Bækurnar eru... = The books are...

So eru agrees with the plural subject.

Because fimm is a numeral, and numerals from five upward do not usually change for gender in normal modern Icelandic usage.

So:

• fimm bækur = five books
• fimm bílar = five cars
• fimm hús = five houses

The word fimm stays the same.

This is different from some lower numbers, especially one to four, which often do change according to gender and case.

Because fimm is not an adjective that agrees like a normal descriptive word.

A learner might expect something like adjective agreement, but numerals do not work that way here. Fimm stays fimm.

Compare:

• góðar bækur = good books
  Here góðar changes to match the feminine plural noun.
• fimm bækur = five books
  Here fimm does not change.

So Bækurnar eru fimm alls is correct, not Bækurnar eru fimmar alls.

Here alls means in total, altogether, or all told.

So the sentence means something like:

• The books are five in total
• There are five books altogether

It adds the idea of the total number.

In this sentence, alls is being used adverbially, not as a normal adjective. You do not need to analyze it as if it were directly describing books. It is best learned as a common word used in counting totals.

Because Icelandic often places short adverbial words like this after the main information.

In Bækurnar eru fimm alls, the core statement is:

• Bækurnar eru fimm = The books are five

Then alls adds altogether / in total.

Putting alls at the end sounds natural and gives a sense of summing things up.

You may also see other word orders, for example:

• Bækurnar eru alls fimm
• Alls eru bækurnar fimm

These are similar in meaning, but the emphasis shifts slightly.

Yes. Bækurnar is the subject of the sentence, so it is in the nominative case.

The sentence structure is basically:

• Bækurnar = subject
• eru = verb
• fimm = predicate numeral
• alls = adverb meaning in total

Since the books are the thing being talked about as the subject, nominative is the expected case.

It is grammatical and natural, but it is not the only natural way.

Depending on context, Icelandic speakers might also say:

• Það eru fimm bækur alls. = There are five books in total.
• Bækurnar eru alls fimm. = The books are five in total.

Your sentence, Bækurnar eru fimm alls, is fine, especially when the books have already been mentioned and you are stating the total number of them.

So the choice depends on what you want to emphasize:

• Bækurnar... focuses on the books
• Það eru... is more like a neutral there are... statement

It is very close in meaning, but the structure is different.

Literally, Icelandic says something more like:

• The books are five altogether

But in natural English, we usually say:

• There are five books altogether
• The books number five altogether
• The books are five in total

So the meaning is the same, even though English prefers a different sentence pattern.

Because the noun is already the subject: bækurnar.

In English, we often count with the noun right after the number, as in five books. But here Icelandic has already identified the noun phrase:

• Bækurnar = the books

So after that, the sentence only needs to state the number:

• eru fimm = are five

That is why you do not need another bækur after fimm.

The singular forms are:

• bók = book
• bókin = the book

The plural forms are:

• bækur = books
• bækurnar = the books

So this noun changes quite a bit between singular and plural:

• ó becomes æ
• the plural stem is bækur
• then the definite ending gives bækurnar

This is a good noun to memorize as a full set rather than trying to guess every form.