The easiest way to discover that specific info is to order their service records from the link at the top of this page. Please note that some service records are expansive (the minority), while most are relatively brief.
When you get their service records, you can then compare what you have discovered about them with what you have found out about the regiment and concatenate the two to figure which battles and actions your ancestors likely took part in.
Also, you can see a capsule history for this regiment at www.mississippiscv.org.
The MS Dept. of Archives & history has Binford's "Recollections of the Fifteenth Regiment of Mississippi Infantry, CSA." (Pat Henry Papers)
Benjamin R. Wayne wrote a thesis entitled "The Fifteenth Mississippi Infantry: A History, 1861-1865." It's at Mississippi College in Clinton, MS.
There is also a publication of some sort entitled "Long Creek Rifles: A Brief History." It was published at Sallis, MS, in 1910 by the Long Creek Rifles UDC Chapter. The MS Dept. of Archives & History is supposed to have a copy of this, too.
Hope this helps.