Translation:In this library, there are five hundred books.
In "proper" English it'd have to be "In this library there are five hundred books" or "There are five hundred books in this library" or "Five hundred books are in this library" although the last one kind of suggests you're primarily describing the location of 500 books, possibly out of a larger number of books ("and seven hundred are in that other library"), whereas the other two are centring the library. But your sentence is certainly understandable.
Actually, it is perfectly correct in English to invert the subject and the verb in such a way; see this particular example from “Subject–verb inversion in English”, as it is similar to Ben813848’s sentence:
In the vase are some flowers.
Notice that this would not be possible with a “weak definite pronoun”:
In the vase are they. → incorrect
Also possible with the item selection list is "In this library are 500 books." The "I" in "In" is also capitalized, whereas the "t" in "this" is not. [I know Duo doesn't care about capitals in the typed answer, but that is usually correct in the item list.] So why is this answer incorrect? [About the only guess I can make is that there is a の between 500 and books. I would think it is, however, too far away from "library" to be a possessive (the library's books, aka the library "has/owns" 500 books).