How can I reduce the size of a continually growing Mail app on my iPhone 5? I have two email accounts on my iPhone: Cox and Gmail.
Each accounts have few messages in their respective Inbox.  No attachments.
The Draft, Sent, and Trash folders are empty.
Yet, with time, the size of this app continues to grow and take up more of the free space on my iPhone 5: and its size is limited, the 16 GB model,
of which 12.5 GB is available to the user.  I am running iOS 8.4.1.

It's as if there is garbage collection that isn't taking place and the storage space doesn't get freed-up.  Think about how hard drive space may get freed-up after sectors are freed-up when you defrag a Windows hard-drive.
Battery Doctor helps free up cache space, etc., but does not affect the Mail app.  My Mail app now takes up 3.0 GB of space!

I have tried removing the accounts, and then setting them up fresh, but this doesn't help… the space is still taken.  I have performed factory resets on the iPhone where it is wiped clean and then have all apps reinstalled, but the problem still exists.  And, so far, I do not have a program that saves my Notes off to my laptop and maintains the formatting of the text, e.g. Bold, Italic, carriage returns, etc.  So, trying to recover the iPhone to the way it was is a real hassle, and the Mail app doesn't reduce in size… it will continue to grow.  Any ideas?
Delete App Mail, just delete. Reinstall the Mail app. Add your email accounts and the hidden hidden storage will disappear