The battle with the dragon is the last battle of Beowulf's long life; he has lived through many adventures and battles, and become a beloved king of the Geats. The text claims that he ruled for "fifty winters," which would make him fifty years older than he was after the battle with Grendel and Grendel's mother. This puts his final age between seventy and ninety years old, depending on his age when he assumed the throne. If he was between twenty-five and thirty-five -- a normal man's physical peak -- when he battled Grendel, then at his death, this age would seem appropriate.
Beowulf spoke, and made a battle-boast, his last one of all: "I have survived many wars in my youth, and now I, the old defender of the people, will once again seek battle and accomplish mighty deeds, if that fell destroyer will come forth from his cavern to fight me!"
(Beowulf, eNotes eText)
His age at death probably can't be pinpointed any closer than that, although a scholar of Old English may be able to gather contextual clues in the text for a more accurate figure. It is safe to place Beowulf's age at around eighty-five at his death, since this would give him time to gain a reputation before fighting Grendel, and then allow him the fifty years of rule over the Geats.
When teaching Beowulf, I usually estimate Beowulf's age at the time of his battle with the dragon to be about 75. Since the poem tells us that "fifty winters" have passed, we obviously know that it has been 50 years since he left Denmark after saving the Danes from Grendel and his mother.
Since we don't know how old Beowulf was at the time of his famous battles in defense of Herot, we cannot really be sure of his age when he fights the dragon. But we do know that Beowulf was still an exceptionally powerful warrior when he fought for Hrothgar in Denmark, and it is never stated that this was surprising because of his age—we expect people to be stronger in young adulthood.
There is also little specific mention of Beowulf's activities before coming to Herot. We know that he had a famous swimming match against Brecca (which he lost), and we know that he has performed valiantly in battle, but there is nothing to suggest that he has been alive for a long time.