Learn Russian: Мне ровно пять лет.

In Russian, you don't say "I am X years old." Instead, the structure is literally "To me are X years." Мне is the Dative case form of я (I), meaning "to me."

Why is the word for "years" лет here? I learned that "year" is год.

The word for "years" changes depending on the number before it. For numbers 5 through 20 (including пять), and any large number ending in 5, 6, 7, 8, 9, or 0, you must use лет. You only use год for numbers ending in 1, and года for numbers ending in 2, 3, or 4.

Where is the verb "am" in this sentence?

Just like with basic descriptions, Russian usually leaves out the verb "to be" in the present tense. The sentence is literally just "To me exactly five years." If you were talking about the past ("I was five"), you would need to add a past-tense verb: Мне было пять лет.

How does the word ровно work here?

ровно means "exactly." You place it right before the number to emphasize the exact amount. It is also very commonly used when telling time, like saying "exactly at five o'clock."