Generally, you should start from the highest order interactions. You are probably aware that it is usually not sensible to interpret a main effect A when that effect is also involved in an interaction A:B. This is because the interaction tells you that the effect of A actually depends on the level of B, rendering any simple main effect interpretation of A impossible.
In the same way, if you have factors A, B, C, then A:B should not be interpreted if A:B:C is significant.
Thus, when you have a 5-way interaction, none of the lower-order interactions can be sensibly interpreted. Therefore, if I understand you correctly and you have interpreted your lower order interactions, you should probably not continue along those lines.
Rather, what you can do is to split up your data set and continue to analyze factor levels of your data set separately. Which of the factors you use to split up the dataset is arbitrary, but often it is very useful to split up the data for each variable and assess what you see. In your example, you might start with sex, and calculate an ANOVA for males, and another one for females (each ANOVA contains the 4 remaining factors). Just as well, you could split up the data according to ethnicity (one ANOVA for Asian, one for Caucasian).
You could also split up by one of the within-subject factors.
I will assume that you have decided to split the data by sex (just to continue with the example here).
Then, assume that for males, you get a 4-way interaction. You would then go on to split up the male data by one of the remaining variables (say, ethnicity). You would then calculate ANOVAs for male Asians (over the remaining 3 factors), and for male Caucasians.
Importantly, if you get only a lower-order interaction, then you are only "allowed" to analyze these further. This is because the other factors did not show significant differences. Thus, if your males ANOVA gives you only a 2-way interaction, then you would average over the other factors and calculate only an ANOVA over the 2 interacting factors (and, because we are in the male part of the ANOVAs, this would be for the males alone).
For the females, everything may look different, and so the decision which follow-up ANOVAs to calculate is separate for this group. So, what you did for males should be done for females in the same way ONLY if you got the same interactions.
Thus, you will potentially have a lot of ANOVAs, and it might not be easy to decide which ones to report. You should report 1 complete line down from the hightest interaction to the last effects (possibly t-tests to compare only 1 of your factors at the end). You should not usually report several lines (e.g., one starting the split-up by sex, then another one starting by ethnicity). However, you must report a complete line, and cannot simply choose to report only some of the ANOVAs of that line. So, you report one complete analysis, not more, not less. Which way to go in terms of splitting up / follow-up ANOVA is a subjective decision (unless you have clear hypotheses you can follow), and might depend on which results can be understood best etc.
Although this is five years late, I will post as an FYI for anyone else who happens to stumble upon this thread. The first part of the model is properly specified, i.e.
time ~ pres*fact*size
However, the error term is incorrectly specified. Note that in repeated measures ANOVA, "the error term for any within-subject effect is the interaction of that effect with subjects [or whatever entity that is repeatedly measured] (Keppel, G., & Wickens, T. D., 2004, p. 40)."
For this particular example, if using R's aov() function, the error term would be specified as such:
Error(subj/(pres*fact*size))
So in all, we have:
m2 <- aov(time ~ pres*fact*size + Error(subj/(pres*fact*size)), data = data)
WRT the interpretation of a three-way interaction: The implication is that a two-way interaction varied over the levels of a third factor. In other words, there was a two-way interaction that was only manifest at a specific level or levels of a third factor. To get to the heart of the matter, you would need to follow up your omnibus ANOVA with interaction contrasts. To determine what interaction contrasts you should test, it would be helpful to plot your data using a line graph. As it stands, there is not enough information available in your post to provide further guidance.
Edit Perhaps it goes without saying, but this is in the case that you obtain such a result with the model properly specified.
Best Answer
A three way interaction means that the interaction among the two factors (A * B) is different across the levels of the third factor (C). If the interaction of A * B differs a lot among the levels of C then it sounds reasonable that the two way interaction A * B should not appear as significant. This could be the case of your data.
To put it another way: A two way interaction A * B exists in reality (not statistically) along with a three order interaction A * B * C only if the way that the factors A and B interacts among the levels of the factor C is similar.
So, use a table or an appropriate error chart in order to visualize the way that the interaction of A, B differs between the levels of C and try to interpret those findings.
If you want to emphasize the differences that you will notice then you may apply standard statistical methods (t - test, Kruskal Wallis etc) and confirm the differences with a statistical test. Keep in mind that in that case it is a good idea to make a Bonferroni correction for the rejection level.