Aragorn was a Dúnedain, a race of men that were directly descended from a more powerful race of men from the continent of Numenor. These people lived much, much longer than the other humans in Middle Earth. In Lord of the Rings: The Two Towers, he tells Eoywn that he's 87 years old just prior to the Battle of Helm's Deep. (As described in this SF&F question, if we go by the novel's timeline, he had actually just turned 88 but we can cut him some slack.)
We known from the films that Lord of the Rings takes place some indeterminate time after Bilbo's 111th birthday, and that Bilbo was in his 50s when The Hobbit takes place. (I'm not sure if the movie specifically gives his age, but it's his 50th birthday in the book). That means Aragorn would be about in his early to mid 20s during the The Hobbit: Battle of the Five Armies.
On a side note: Lord of the Rings: The Fellowship of the Ring condenses the early timeline a good deal. It's not obvious from the movie, but there's a long time between Bilbo's birthday and the coming of the Nazgul to The Shire -- 17 years, in fact.
By the book's calendar, Aragorn was born in 2931, and the Battle of the Five Armies happened in 2941, so Aragorn would have been 10.