Using "summon Item @a {Age:5680,Item:{id:minecraft:stick}}" produces a stone block item at command block.
Comments 2
Confirmed. Stone is the default for Item, and so getting it when you're not supposed to usually means your code is wrong and everything in brackets is being ignored.
Wait...it's a summon command not a give command. Why do you have @a? That would be the bug. The code you're using is being interpreted as "summon Item". Replace the @a with co-ordinates (using "~ ~ ~" as the co-ordinates makes it appear inside the command block). Also if you don't include a count then it will be a ghost item (stack of zero items). Corrected code would be:
"summon Item ~ ~ ~ {Age:5680,Item:{id:minecraft:stick,Count:1}}"
Cannot reproduce or confirm.