The new (not legacy calendar) in APEX 5 comes with a set of default calendar CSS classes to style calendar events. The following screenshot is from the inline help for the calendar CSS Class attribute:

{% asset_img calendar-help.png "" %}

I couldn't find how to create a custom class in the documents (as the help suggests). Using the pre-defined classes as an example I was able to create a custom class for a new color for my calendar. The following is an example of a custom APEX calendar class:

.fc .fc-event.apex-cal-demo {
  background-color: #F0F8FF;
  border-color: #000000;
  color: #FFFFFF;
}

In the calendar query this class can now be referenced as apex-cal-demo.