Sharon,

Chaim D. Greenberg enlisted in The U.S. Army June 11, 1898.
He served during The Spanish American War.
He appears to have been, at one point, in the hospital corps at Montauk (out on Long Island, NY)
His rank was Private.
He served in Company K, Regiment 7th infantry.
A mention of Josiah Simpson Hospital in VA is noted.
He was discharged Nov. 7th, 1898.
 
Above info from Ancestry.com database:
U.S., Army, Register of Enlistments, 1798-1914

He possibly served at  Camp Wikoff (Montauk Point, Long Island, New York)
This site describes the hospital set up for returning soldiers and has a photo.
https://www.spanamwar.com/campwikoff

The card that you scanned to your post is from the Ancestry database titled:
U.S., Civil War Pension Index: General Index to Pension Files, 1861-1934
The title is misleading, since it includes not only Civil War pensions, but also a general index to pension files.
Chaim D. Greenberg applied for a pension in 1930 and received it in 1931.  He served in The Spanish American War (not The Civil War, as he was not even born during the time of that war in the first half of the 1860's.)

Chaim is also listed in the Ancestry database:
U.S., Army, Register of Enlistments, 1798-1914
There is a lot of information if you look at the actual page in the database.
He was born in Minsk, and lots of other info, including a mention of being at Josiah Simpson Hospital in VA, which his other card mentioned (noted above.)

Good luck in your search,

Sherri Bobish

Searching:
RATOWSKY / CHAIMSON (Ariogala, Lith.); LEFFENFELD / FINK / KALTER (Daliowa & Jasliska, Pol.)
BOJDA / BLEIWEISS (Tarnow & Tarnobrzeg, Pol.); WALTZMAN / WALZMAN (Ustrzyki Dolne, Pol.)
LEVY (Tyrawa Woloska, Pol.); SOLON / SOLAN / SOKOLSKY (Grodek, Bialystok, Pol.)
BOBISH / BLUMENKRANZ / APPEL / WEINER / ROSENBERG (Vysoko-Litovsk, Brest, Biala Podlaska)