Regular 503 error every 5 minutes for logged in users

From my experience, you had far, far too many plugins. Disable everything, choose one of the twenty**** default themes and try again.

You should also check your server log and see if you can see anything in there that would help (and post it here).

Lastly, take a backup of your entire site (code, uploads, database) and then do a clean install of the latest WordPress release with a clean database and see if you still get an issue. It could still be a problem with your hosting or some configuration on your account.