Thranduil mentioning Strider (Aragorn) at the end of the third Hobbit movie

Due to his Númenórean decent, Aragorn is around the age of 87 during the events of The Lord of the Rings. When he is crowned king of the Reunited Kingdom, his reign lasts a whopping 122 years, until his death at the age of 210.

As such, given the events of The Hobbit occur around 60 years before The Fellowship is formed, that would put Aragorn somewhere around his late 20s when Legolas is told to meet him.

Battle of Five Armies occured in 2941 T.A. while Aragorn was born in 2931 T.A. Therefore he is born already but only 10 years old at the time.

Sources:

http://lotr.wikia.com/wiki/Battle_of_Five_Armies#cite_note-0

http://lotr.wikia.com/wiki/Aragorn_II_Elessar

(You can google other sources but they all agree to this)

Many people doubt Jackson would allow for such mistake (What Thranduil says doesn't make any sense if Aragorn is 10) But considering other plot holes and overall quality of this last installment of the trilogy, it may actually be the case.

Aragorn is a Dúnadan, a descendant of the people of Númenor. Their lifespans are much longer than those of other (normal) humans.

According to Wikipedia, Dúnedain of high rank -like Aragorn- have lifespans three times as long as normal humans.

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.