Google Calendar Events – Scheduling Events for the Last Sunday of Each Month

Although Google Calendar doesn't allow you to create or modify arbitrary recurrence rules, the iCalendar specification which it uses and understands is quite robust in this regard.

Create an ICS file with a custom recurrence rule (RRULE). For example, for an all-day event on the first, third, and fifth Fridays of every month, starting 2 March 2012:

BEGIN:VCALENDAR
BEGIN:VEVENT
DTSTART;VALUE=DATE:20120302
DTEND;VALUE=DATE:20120302
RRULE:FREQ=MONTHLY;INTERVAL=1;BYDAY=1FR,3FR,5FR
DESCRIPTION:
LOCATION:
SEQUENCE:0
STATUS:CONFIRMED
SUMMARY:Event on the first, third, and fifth Fridays.
TRANSP:TRANSPARENT
END:VEVENT
END:VCALENDAR

To import the ICS file (updated June 2018): Click the gear icon and select "Settings", then choose "Import & export" from the menu. (Here's a direct link as of June 2018.) Under "Import", select your ICS file and upload it to the desired calendar.

For this example, Google Calendar parses the RRULE correctly and even describes the recurrence as "Monthly on Friday of weeks 1, 3, 5 of the month":

Of course, you won't be able to tweak the custom recurrence rule from within Google Calendar, unless you want to replace the recurrence rule entirely with one of the standard options. Otherwise, you'll have to delete the event, tweak your ICS file, and reimport. You should still be able to make other changes to the event within Google Calendar, such as renaming, moving to another calendar, etc.

If this helps, you may wish to read more about the flexibility offered by custom recurrence rules in the iCalendar specification.

Your best bet is to create five separate annually repeating events (as you mentioned). It takes about 1 minute per event and you're done with it for life.