Why does my rear #5 cylinder run hot? 337B
 

Why does my rear #5 cylinder run hot?
In cruise the EGT runs on avg 100 F hotter than next hottest cylinder.
How do you fix this?

Things to look at
 

I can't speak to any peculiarities of the 337 but in general here are some things that can lead to a single cylinder running hotter that I have used myself and recommended to other owners over the years as an A&P. Hopefully it is something simple for you.

1) If CHT stayed the same, or just changed a few degrees and just the EGT went up you may have a failed spark plug. This is generally apparent on a mag check though.
2) A dirty fuel injector could be the culprit. Pull the insert, soak it in some Hoppes #9 gun cleaner or MEK, and make sure it isn't obstructed. It's ok to put it in an ultrasonic cleaner too if you have one. Under no circumstances stick anything into the orifice to clean it. I have had to tell customers in the past they needed new injector bodies because they thought they could use safety wire to try to clear a blockage. Just be careful with this one and seek the supervision of an A&P since pulling and re-installing a fuel injector body is not covered under the preventative maintenance section of 14 CFR part 43.
3) Could be the sign of a failing probe. Move the probe to another cylinder and see of the problem moves with it.

Hope I haven't just re-stated the obvious or things already known.

Eric