Dit is de vijftiende vraag.

Because dit here is a standalone pronoun, meaning this in This is the fifteenth question. It is not directly attached to vraag.

If you put the demonstrative directly before the noun, then you would use deze because vraag is a de-word:

• Dit is de vijftiende vraag. = This is the fifteenth question.
• Deze vraag is de vijftiende. = This question is the fifteenth one.

So the key difference is:

• dit = used on its own
• deze = used directly before a de-word noun

Because vraag is a de-word in Dutch. Its definite article is de.

You usually have to learn Dutch nouns together with their article:

• de vraag = the question

There is no simple rule that always tells you whether a noun is a de-word or a het-word, so learners often just memorize them case by case.

Vijftiende is the ordinal form of vijftien:

• vijftien = fifteen
• vijftiende = fifteenth

Dutch ordinal numbers are often made by adding -de or -ste, but the pattern is not completely predictable for every number, so it is worth learning the common ordinal forms as vocabulary.

A few examples:

• vier → vierde
• acht → achtste
• tien → tiende
• vijftien → vijftiende

Because the correct Dutch ordinal for 15th is vijftiende. Not all Dutch ordinals use -ste.

A rough pattern is:

• many lower and teen numbers use -de
• some others use -ste

But there are enough exceptions and fixed forms that it is safest to learn them individually, especially the most common ones.

So for this sentence, only vijftiende is correct.

The structure is very close to English:

• Dit = subject
• is = verb
• de vijftiende vraag = complement

So the pattern is:

subject + verb + complement

That is why it feels quite familiar to an English speaker:

• This is the fifteenth question.
• Dit is de vijftiende vraag.

Yes. It is an ordinal numeral, but in this sentence it behaves like an adjective in front of the noun vraag.

Compare:

• de eerste dag = the first day
• de tweede keer = the second time
• de vijftiende vraag = the fifteenth question

So although it is a number word, it functions grammatically much like an adjective before the noun.

Yes, in some contexts you can, especially when talking about numbered exercises, test items, or questionnaire items.

There is a small difference in feel:

• de vijftiende vraag = the fifteenth question
• vraag vijftien = question fifteen / question number fifteen

The original sentence sounds like normal descriptive Dutch. Vraag vijftien is also common, but it can sound a bit more like labeling or numbering.

• dit = this
• dat = that

In many situations:

• dit refers to something close, present, or being introduced
• dat refers to something farther away or already mentioned

Examples:

• Dit is de vijftiende vraag. = This is the fifteenth question.
• Dat is de vijftiende vraag. = That is the fifteenth question.

In real conversation, the difference is often based on context, not only physical distance.

A rough English-friendly guide would be:

• Dit ≈ dit with a short i
• is ≈ iss
• de ≈ duh when unstressed
• vijftiende ≈ VEIF-teen-duh (very rough)
• vraag ≈ vraakh, with a throaty final sound

A few pronunciation notes:

• ij in vijf is a Dutch vowel sound that does not match English perfectly.
• The g in vraag is the guttural Dutch sound also heard in goed or dag in many accents.
• de is usually weak and unstressed in normal speech.

So the whole sentence is roughly:

dit iss duh VEIF-teen-duh vraakh

That is only an approximation, but it is a useful starting point.