Hi Bruno
I finished doing some basic research on the 5th BI and it appears that it served with the III Army for the entire war and after the Battle of Sedan was involved with the Siege of Paris. I'll note below some casualty returns which will give an idea of the regiments activities.
Battle of Worth, 3 killed, 35 wounded, 1st & 2nd Btl engaged
Battle of Sedan 1 killed, 3 wounded
Drive on Paris, battles Petit Bicetre & Chatillon 1 killed, 6 wounded 1st & 2nd Btl.
Investment of Paris
21 September 4 wounded
27 September (3rd Battalion assigned to 8th Brigade) 2 wounded
Battle of Chevilly 1 killed, 7 wounded
Battle of Bagneux 9 kiled, 9 wounded
19th October 4 wounded
7th January 1871 4 wounded
8th January 2 wounded
9th January 2 wounded, 1 missing
15th January 2 wounded
17th January 1 wounded
The total casualties for the IInd Bavarian Army Corps were 808 killed, 2582 wounded.
The 3rd battalion of the 5th Regiment seems to have been attached to the 8th Brigade for the better part of the campaign.
Best Regards
Larry