Even with WiFi turned off it is still the biggest battery drainer (S5 Mini)
Navigate to Settings -> WiFi -> Advanced (under the context menu) and ensure that Scanning always available is not checked. This feature 'Let's Google location service and other apps scan for networks, even when WiFi is off'.

This is most likely the cause of the battery drain. To further reduce WiFi battery use, you could change the Keep WiFi on during sleep option to Only when plugged in or Never. However, this may prevent you from receiving emails, messages and similar notifications while the device is locked.