Learn Turkish: Yaşlı adam düşüyor.

It comes from the verb root düş- (to fall). Because the root ends in a consonant and its vowel is ü, we add the matching present continuous suffix -üyor to get düşüyor (he/she/it is falling).

Can I use yaşlı to say my car or phone is old?

No, yaşlı is only used for living things, like people or animals. It literally means "with age" (the word yaş means age). For objects, you must use the word eski.

Where is the word for "the" in this sentence?

Turkish does not have a direct word for "the". The phrase yaşlı adam can mean "an old man" or "the old man" depending on the context. Here, we know we are talking about a specific man who is falling right now.

Why isn't there a separate word for "is" in the Turkish sentence?

In English, we say "is falling", but Turkish builds that meaning directly into the verb. The present continuous suffix -üyor does all the work, so düşüyor alone means "is falling".