My customer's site has been showing "500 internal server error" few times out of 10 tries. Same problem persist in public web site and admin.
When you get 500 error, you need to reload the page and then all works well. I've noticed that the problem lies in Events manager (disabling it removes errors).
There are roughly 100 events and no advanced features enabled, just viewing events.
WP: 4.0
EM: 5.5.3.1
Php memory limit: 512M
Installed plugins:
Events Manager
Google Analyticator
Maintenance Mode
Types - Complete Solution for Custom Fields and Types
UberMenu 2 - WordPress Mega Menu Plugin
Widget Logic
WooDojo
WooSidebars
WPML Multilingual CMS
WPML String Translation