Hi Tom,
I'm no CFM56 expert but I'd there are a number of possibilities....
1. The higher temperature on the 5C could be result of the increased thrust rating....i.e. pushing the engine harder for a given fan and core size.
2. The temps on the 5A/B cycle could have been lowered in the performance design phase to boost the disc and shaft lives (lower temps = longer life). While not optimal from an efficiency point of view, the A320 doesn't sit in the cruise very long relative to an A340 and so a higher core temp may not provide much benefit in terms of fuel consumption but it would significantly extend the life of the discs and shafts which are life limited by cycles.
I suspect it's a combination of the two.
Cheers,
P2C