Age has no limits. Caleb was 40 years old when Moses first promised him land. After 38 years of wandering in the wilderness and another seven years of war in the conquest of Canaan, he was now 85 and, in his own words:
Joshua 14:11 I am as strong now as I was when Moses sent me on that journey, and I can still travel and fight as well as I could then.
So Caleb asked for the hill country that he’d been promised. Most 85-year-old men would be a bit less gung ho, especially since the Anaks were giants, but Caleb was determined and, just as he did when he was 40, believed God was with him:
Joshua 14:12 So give me the hill country that the Lord promised me. You will remember that as scouts we found the descendants of Anak living there in great, walled towns. But if the Lord is with me, I will drive them out of the land, just as the Lord said.
The actual battle was probably after Joshua’s death (see Judges 1:11-15), and it was possibly one of the last battles (or the last of the victorious battles) as we are told the land then had a rest from war.
The conquest wasn’t yet finished: the land had been allocated, but all of it had not yet been taken in battle or occupied afterwards. This included Jerusalem:
Joshua 15:63 But the tribe of Judah could not drive out the Jebusites, who lived in the city of Jerusalem, so the Jebusites live there among the people of Judah to this day.