Is there any way to reduce an app's usage of storage space on iOS 5?

I believe there is no way for a end-user to do this. All iOS apps will have Application_Home/Documents, Application_Home/Library, Application_Cache folders. All the files stored in these folders should be managed by application itself. So, it's true that you can't do this without jail breaking.

You could delete the Facebook app and then reinstall it. When you delete an app like Facebook, there's a little warning saying that deleting this app "will also delete all of its data", which is exactly what you want.

I just tried this on my iPhone - deleting the Facebook app and reinstalling it made its usage go from 47 MB to 16 MB. This is only a temporary solution of course, since as you use Facebook it'll cache images etc. to speed up your browsing, so it'll start using more space again.

It is definitely possible to access app sandboxes via an AFC client such as iFunBox or iPhone Explorer.

To emulate the criticized aggressive cleaning of iOS 5.0 you would empty the […]/Library/Caches/ and […]/tmp/ directories of the involved app(s), but due to the manual access involved one can perform a finer-grained selection.

The PhoneClean app also performs fully automatic or app selective cache cleaning.