TheCannonballGuy said:Your button is a US Army Enlisted-ranks (private, corporal, sargeant) button, worn by those ranks in all the branches of Army service (artillery, infantry, cavalry, etc.), issued from 1854 through 1874. (In 1875, the emblem was changed slighly, by making the simple striped shield be a "raised" one -- and your button's shield is not raised, so you've dwfinitely got the 1854-to-1874 version.)
Because tens-of-thousands of this button were "left over" as un-needed surplus when the civil war ended, almost none were manufactured after 1865. Therefore, even though the backmark on your button can no longer be read, the odds highly favor it having been manufactured sometime between 1854 and 1865.
TheCannonballGuy said:First... please keep in mind that the date-range I was speaking about is for the raised "striped-with-no-letter" shield on the 1854-1874 Army Enlisted-man's buttons. There are some shield-with-letter versions which are earlier than 1854.
Now, answering your question "What years were the [striped-with-no-letter] raised shield used?":
The answer is 1875-to-1902. (In 1902, the emblem was radically changed.)
Here's a photo showing the 1875-to-1902 version. I hope it shows "well enough" that its striped no-letter shield sticks up higher than the body of the eagle.
By the way, unlike on the civil war era "eagle buttons," the 1875-1902 eagle's shape somewhat resembles a spread-winged chicken, so button-collectors sometimes call these Indian Wars era buttons the "chicken eagle" button.