Mike
As you've stated, the 5th (along with 2nd & 4th, and the 4th Battalion The Buffs) was part of the
133rd Infantry Brigade
The 133rd was at the following places:
and was subordinate to the following units:
Depending upon when your chap died, one could narrow down where the 5th was, and what they would have been participating in.
The above details come from:
http://www.ordersofbattle.com/