I have taken a DNA test, and found out I shared over a percentage of DNA with a person. Through church records I found out that we are 5th cousins, - but doubly in the last generation, i.e., we have two sets of shared 4xgreat grandparents. If we had only one set, our shared DNA should have, on average, been 0.04% which is 25 times less.
I am sure that other factors (kinship I don't know, measurement errors at the website, the fact that the amount of DNA passed down in each generation obviously differs (law of great numbers), etc), matter, but it makes me curious about what the theoretical average shared DNA between us would be. You can't simply double the kinship for 5th cousins, can you? You need to do something fancier, methinks.