5-way interaction I am running a mixed factors ANOVA for a brain imaging study on language processing. The design includes four within-subject factors:


*

*complexity: simple/complex;

*agreement: correct/number violation/gender violation; 

*hemisphere: left/right;

*region: anterior/posterior; 


and one between-subject factor:


*

*proficiency: low/high proficiency. 


Factors 3 and 4 (hemisphere, region) only matter if they interact with the other factors. This is because the effects of complexity and agreement are predicted to emerge in specific areas of the scalp.  
The results reveal a significant 5-way interaction (complexity by agreement by hemisphere by region by group), and I find it almost impossible to figure out what is driving the interaction by just looking at the means. 
Am I justified in looking at the two proficiency groups separately? Most similar studies do this, but I'm unclear as to how to do this. For example, once I decide to examine proficiency learners separately, I find a 3-way interaction between agreement, hemisphere, and region in the high-proficiency learners (meaning that there is a brain response for agreement violations, which is captured in the left anterior portion of the scalp), but there is no such interaction for low-proficiency learners (p = .13) Is it licit to report this difference even if the original omnibus ANOVA (with group as a factor) showed that there was no agreement by hemisphere by region by proficiency interaction? 
In other words, once I decide to look at the two proficiency groups, can I run the analysis as if I had never compared the two groups or am I constrained by the original ANOVA as to what follow-ups I can do?
 A: Without the numbers I can just give the general advice, graph it.  You have 2 x 3 x 2 x 2 x 2 so that's not that hard.  Take one of your 2 level variables and calculate it's effects across everything else.  That's what you'll plot.  You can now plot 3x2 or 2x3 panel graphs.  You'd have 4 panels with the remaining two  factors crossing them, one divided horizontally, and the other vertically.
Stare at that for awhile.
Maybe several permutations.  Change what's on the x-axis, the panels, line types, and effects through as many iterations as you need until you come to an understanding.  If you've got some theoretical reasons for directions of causality take the highest level and make it panels and the lowest and make it your line types or x-axis.
Hopefully you'll come up with something.  This could take a lot of work and a long time to see the nature of the relationship.  But going through several versions of the graphs can often allow you to see what's going on.
(I recently had to do the same thing for 10 x 3 x 2 x 2 x 2. It took months looking at graphs off and on and letting them incubate before the nature of the 5 way came through.)
UPDATE:I just noticed your question on splitting by proficiency.  What you described is an absolute no-no.  An interaction in one proficiency group while none in another does not tell you that there are differences between those groups. An interaction with proficiency would. So leaving proficiency out of your interactions gives you much less information. Your interactions mean something and the meaning is in the data, not in more tests.
As I ask most of my students, if you're going to test everything afterwards what was the point of doing an ANOVA in the first place?
