A library has conducted a survey of its readers. The survey asked its $10,000$ readers about their reading habits and the number of books that they have borrowed from the library in $2012$. It has found that its readers claimed to have borrowed $75,000$ books in $2012$. The library has also reviewed the borrowing records of its books and found that on average a book was borrowed $5$ times. The library has $20,000$ books.
Is this survey accurate?