Make it 165
This is ridiculous advice. Sorry but it is.
Yeh 125/call or shove.
Tbh Alex, although it is very close (given that stack sizes are a little over 100bbs) there is not quite enough wiggle room to make a leveraged 5bet. If stacks were deeper we could find an extra leverage point, but not here. So we are left with either jamming or flatting...
Is 5 betting all in always the correct play here?
Yes it is the correct play. But it is not the only correct play. Despite a generally held belief amongst multi-tabling grinders that you can't flat 4bets and are shove or fold, theory says that we
should have a flatting range IP when opponent makes a
very small 4bet (and by 'very small' I mean a CIB or similar. I
don't mean a standard small 4bet of just under a quarter of effective stacks). And this is even more so when we are slightly deeper than 100bbs.
You can do some work with pokerstove and a calculator and come up with a flatting range in these spots. It is important to look at stuff like this and have a grasp of your ranges, even though in game you will likely decide more on instinct. If you have access to Bluefire there was a very good video a few years back with Phil Galfond discussing flatting 4bets when ~100bbs deep.
BTW, just re-read this and it seems like I am advocating always flatting KK here. I am definitely not doing so... I would jam far more often than flatting.