Min fødselsdag er den 5. maj, og min søsters er den 12. august.

Because Danish, like German, very often forms nouns by combining words into a single compound.

• fødsel = birth
• dag = day
• fødselsdag = birthday

English sometimes uses separate words where Danish prefers one compound word. So birthday and fødselsdag work in a similar way.

Danish possessives agree with the grammatical gender/number of the noun:

• min for common gender singular nouns
• mit for neuter singular nouns
• mine for plural nouns

Fødselsdag is a common gender noun, so you say min fødselsdag.

The same applies in min søsters ... because søster is also common gender.

In Danish, dates are commonly expressed with den + ordinal date + month.

So:

• den 5. maj = the 5th of May
• den 12. august = the 12th of August

This is the normal way to say a calendar date in a full phrase. English often includes of in explanations like the 5th of May, but Danish does not need a separate word like of here.

The dot shows that the number is being used as an ordinal number, not just a plain cardinal number.

So:

• 5. = fifth
• 12. = twelfth

That is why den 5. maj means the 5th of May, not just the 5 May.

In Danish, names of months are normally written with lowercase letters.

So:

• maj
• august
• januar
• februar

This is different from English, where month names are capitalized.

Danish forms the genitive, or possessive, by adding -s directly to the noun, usually without an apostrophe.

So:

• min søster = my sister
• min søsters fødselsdag = my sister's birthday

English uses an apostrophe, but Danish usually does not.

Because the noun is understood from the first part of the sentence.

The full version would be:

• Min fødselsdag er den 5. maj, og min søsters fødselsdag er den 12. august.

But repeating fødselsdag would sound unnecessary, so Danish leaves it out. English does the same kind of thing:

• My birthday is May 5th, and my sister's is August 12th.

So min søsters here means my sister's birthday, with fødselsdag understood.

Because er is the verb, and Danish normally puts the verb in the second position in a main clause.

The structure is:

• Min fødselsdag = subject
• er = verb
• den 5. maj = complement

So the sentence follows very normal Danish word order.

In some contexts, you may hear or see dates written more briefly, but den 5. maj is the standard full form in a sentence like this.

So for learners, it is best to use:

• Min fødselsdag er den 5. maj.

That will sound natural and correct.

Yes, it can be tricky for English speakers.

A few points:

• fø contains the Danish vowel ø, which does not exist in English.
• The d in -dag is often softer than an English d.
• Danish words often have reduced or softened sounds in normal speech.

You do not need perfect pronunciation immediately, but it helps to notice that Danish pronunciation is often less phonetic than spelling suggests.

Og simply means and. It joins the two clauses:

• Min fødselsdag er den 5. maj
• min søsters er den 12. august

This is completely normal Danish usage. One thing learners should notice is that Danish often keeps sentence structure quite parallel when joining two ideas like this, even if part of the second clause is omitted because it is already understood.