The ratio of borrowed books to the remaining books is 5: 6.

Then the number of books borrowed is 5/(5+6)=5/ 1 1.

So 60 is 5/ 1 1-2/5=3/55 of the total.

The total number is: 60/(3/55)= 1 100.

There are books in the library: 1 100*6/(5+6)=600.