Original loading was with a 227-grain .322" RN bullet at 2100 ft/sec MV (figures from TBSA-1909). Troubles with unstable powders led to chambers lifting out, which gave rise to the "neues muster" or "nm" rifles, which had much heavier chamber sections.
Gew 88/05 should be reamed for the JS loading: 154-grain .323" pointed bullet at 2880 ft/sec MV.
Note carefully that this is NOT the JsS load: that was developed strictly for anti-Tank use. It had the 196 BT slug running at over 2600.
The SmE and SmK which were used so much in War Two had 178-grain BT slugs and were very hot loadings.
As already suggested, standard Amerfican 8mm Mauser ammo is loaded down far enough you should have no troubles.
Stay away from military ammo, also from those very-hot European loadings. An 88/05 is too nice to take silly chances with, ESPECIALLY if you don't have the "nm" rifle with the heavy chamber.