Size of vocabulary of highly educated Chinese person
What differentiates Chinese characters from English words is that most Chinese characters are not only words but also morphemes. 

e.g.


  In the English word unlikely, there are three morphemes, un, like and
  ly, but only like is a word. 
  
  In this Chinese compound word 不可能, there are also three morphemes,
  不、可、能, but each of them constitutes a word.


The estimated 5000-word vocabulary is not an indicator of the number of words like 不可能 one masters, but of morphemes like 不、可、能. 

A senior high school student is requested to master at least 6600 common characters. A Ph.D. is likely to have a similar, if not higher, vocabulary, as however difficult the jargons he possesses are, these jargons can be translated into Chinese with common characters, for example, polychlorinated biphenyl is translated as 多氯联苯, which every junior high student should be able to recognize but perhaps not fully understand.