The methods section of the study I linked begins as follows:
Testing reported herein was conducted in Mayand June of 1999. Testing
was done individually for children in kindergarten through Grade 2. The
investigator introduced herself and said
I’m going to ask you what some words mean. Later, I'll ask you to
read the same words and some others. Some of these words are
common and some aren’t. If you want to stop at any time, you can.
I’m going to read you a sentence and then ask you what a word means
in that sentence. You can use words, pointing, or acting to explain the
meaning of that word.
We then gave three examples, including, “ ‘I bought a new car.’ In this
sentence, what does car mean?” We continued with “ ‘Johnny fell and
broke his arm.’ What does arm mean?” If the child had difficulty with these
examples, we would go over them and explain how to answer. (In the arm
example, pointing to one’s arm would do.) A final example involved a hard
word: “ ‘The material was translucent.’ In this sentence, what does translucent mean?” This example was given so that we could explain that there
would be words children did not know, and that it was alright to say, “I
don’t know.” (No children actually knew translucent.)
This seems to me like a test of which words children know, not the range of words typically used.
I can't find the term "expressive vocabulary" anywhere in the paper. Did you assume that's what they were estimating because the number seems low? Actually, 3000 words is quite a lot. The Simple English Wikipedia tries to use only the most common 1500 or so words, for example. Most concepts can probably be expressed in words a five-year old is familiar with. It's just that not everyone takes care to express themselves that clearly, so having a larger vocabulary is still beneficial.