Learn German: Ist der Hund fünf Jahre alt? - Is the dog five years old?

No. Cardinal numbers like fünf (five) don't change their endings when placed before a plural noun. You just say fünf Jahre. The only number that changes its ending is ein (one), which acts like the articles "a" or "an" depending on the noun's gender.

Why is the word for year written as Jahre here?

Because it is plural! Das Jahr (the year) becomes die Jahre (the years) in the plural. Many neuter nouns in German form their plural by simply adding an -e to the end. Since the dog is five years old, we need the plural form.

Why does the sentence start with Ist?

This is a yes/no question. Just like in English, you form a yes/no question by swapping the subject and the verb, moving the verb to the very front of the sentence. The statement "The dog is..." (Der Hund ist...) becomes "Is the dog...?" (Ist der Hund...?).

Does German always use "to be" (sein) for age?

Yes! If you've studied languages like Spanish or French, you might expect to say the dog "has" five years. But German works exactly like English here: the dog "is" five years old (ist fünf Jahre alt).