Let me first re-phrase your question: What is the number of (positive) integers less than 10000 (5 digits) and greater than 999 (3 digits)?
The greatest 4 digit integer would be 9999.
The greatest 3 digit integer would be 999.
Let's do some subtraction: 9999 - 999 = 9000
This works because as we count up from 999, each positive integer encountered satisfies your requirements until reaching 10000.
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The lowest positive 4-digit number is 1000
-22
There are one thousand. Starting at 2000 and going to 2999
-48
5*5*4*4 = 400