"Is a vocabulary of 5,500 words enough for studies at an Australian university?"

The size of your vocabulary is the single best indication of your overall standards.

Take the vocabulary test at your preferred level.

Your "doctor's prescription" course has ...

punkt A guide to building vocabulary
punkt A tool for making your own word list
punkt A tool for making your own tests on your own words
punkt Hundreds of general vocabulary exercises and tests
punkt Very special word formation exercises