~10 years old
According to this article on Bustle he would be around 10 as he "was born in the year 2931 in the era known as “the Third Age.”" and "Bilbo Baggins’ (Martin Freeman) quest to reclaim Lonely Mountain alongside the Dwarves began in 2941, a mere decade later, and lasted approximately 13 months".
Yes, Aragorn would have been around at the time of the Battle of the Five Armies’ conclusion… but he would have been about 10 years old. Aragorn was born in the year 2931 in the era known as “the Third Age.” Meanwhile, Bilbo Baggins’ (Martin Freeman) quest to reclaim Lonely Mountain alongside the Dwarves began in 2941, a mere decade later, and lasted approximately 13 months (he must have used up a ton of vacation days). This, when you consider the lengthy life spans of the humanoid creatures that occupy Middle-earth, would render Aragorn even younger in perspective.
But maybe he’s a quick learner? Well, according to Tolkien’s literature, Aragorn first earned the handle “Strider” in 2956, due to his efforts protecting various pastures in Middle-earth. Ergo, it wouldn’t be for another 15 years that he’d come to occupy the identity referenced by an apparently prescient Thranduil.
Of course, Aragorn and Legolas would eventually come to meet, but a bit of a ways down the line. The Fellowship of the Rings begins its story in 3001, at which point Bilbo would be approximately 111 years old, Aragorn/Strider a youthful 87, Gimli about 139, and Legolas just under three centuries in age. For Hobbits, Men of Middle-earth, Dwarves, and Elves, these numbers don’t exactly scream “post-retirement.”