عدد البطاقات خمسة.

Here, عدد means the number / the quantity / the count.

It is close in meaning to رقم, but they are not exactly the same:

• عدد = number as quantity
• رقم = number as a numeral, figure, or label

So in this sentence, عدد البطاقات means the number of cards, not the numeral of the cards. That is why عدد is the better word here.

Because Arabic often leaves out the present-tense verb to be.

So:

• عدد البطاقات خمسة.
  literally: The number of cards five.
• natural English: The number of cards is five.

This is called a nominal sentence in Arabic.

If you wanted the past tense, Arabic would usually add a verb:

• كان عدد البطاقات خمسةً.
  The number of cards was five.

It is an iḍāfa construction, often called a construct phrase.

So:

• عدد = number
• البطاقات = the cards

Together:

• عدد البطاقات = the number of the cards
  or more naturally in English: the number of cards

In Arabic, this is a very common way to say X of Y:

• باب البيت = the door of the house
• اسم الطالب = the student’s name
• عدد البطاقات = the number of cards

That is because of the iḍāfa structure.

In an iḍāfa:

1. The first noun does not usually take الـ
2. The first noun does not take tanwīn
3. The second noun is put in the genitive

So here:

• عددُ = first noun in the iḍāfa
• البطاقاتِ = second noun, so it is genitive

Fully vocalized, the phrase is:

• عَدَدُ البِطاقاتِ

This is why you do not normally write:

• العددُ البطاقاتُ ❌
• عددٌ البطاقاتُ ❌

This is a very common question.

The short answer is: in this sentence, خمسة is being used as the number 5 itself, not as a numeral directly attached to بطاقات.

So the sentence means:

• The number of cards is five

Here, خمسة is the predicate of the sentence, almost like naming the number 5.

But if you were directly saying five cards, then you would normally use:

• خمس بطاقات

That is because direct counting has its own gender rules. So compare:

• عدد البطاقات خمسة. = The number of cards is five.
• خمس بطاقات = five cards

Fully vocalized, it is:

• عَدَدُ البِطاقاتِ خَمْسَةٌ

Why?

• عَدَدُ = nominative, because it is the subject of the nominal sentence
• البِطاقاتِ = genitive, because it is the second term of the iḍāfa
• خَمْسَةٌ = nominative, because it is the predicate

A basic grammatical breakdown is:

• عَدَدُ = subject (mubtadaʾ)
• البطاقاتِ = genitive complement of the iḍāfa
• خمسةٌ = predicate (khabar)

A careful full pronunciation with case endings is:

• ʿadadu l-biṭāqāti khamsatun

In normal pause, many final short vowels are not pronounced, so it may sound more like:

• ʿadad al-biṭāqāt khamsa

A few pronunciation notes:

• ع in عدد is the Arabic letter ʿayn, which has no exact English equivalent
• الـ in البطاقات is pronounced al-, because ب is a moon letter
• ة in خمسة sounds like -a / -ah in pause, but -tun when fully inflected with tanwīn

It is grammatical, but it is a bit more like:

• The number of cards is five

So it sounds slightly more formal or more focused on the total count.

If you simply want to say There are five cards, a more direct wording is often:

• هناك خمس بطاقات.

So the difference is roughly:

• عدد البطاقات خمسة. = emphasis on the total number
• هناك خمس بطاقات. = straightforward statement that five cards exist

Because Arabic and English do not always use definiteness in exactly the same way.

In Arabic, البطاقات has الـ, and the whole iḍāfa becomes definite. But in English, the most natural translation is often just:

• the number of cards

rather than the more literal:

• the number of the cards

So the Arabic form is definite, but the best English translation may sound less literal. This is very common with Arabic iḍāfa phrases.