Both the public library and your school library are good starts. You cannot also put out an email to parents that you are looking for books. I would also alert churches and other groups in your community of your lack of books, there are many people that want to help a school and are not sure what to do. I would also check around your school and ask other teachers if you could borrow specific titles. I then would review letter writing and have your students write thanks you letters to anyone who brings a book for your classroom.

Another idea, if your school allows this, is to write a grant through Donors Choose. It’s a very easy process, when people who want to support education can donate funds to needy, deserving teachers/school. Check out their website–it’s pretty amazing how fast grants can get funded. I would think supplying books to classrooms would be a easily supported one.
Here’s another one–check our Wilbooks website http://www.wilbooks.com/. They offer great deals on multiple copies of books at VERY reasonable prices. If your school is a Title 1 school, there are a lot of free opportunities.
In my city of San Antonio, there is a charitable group called San Antonio Reads, which offers an amazing amount of free books for schools. Look around your city/town, for such opportunities.
Ask other teachers for extra copies they may have stuck in closets or that they don’t use now. Maybe they won’t be the best choices, but filling up the shelves will let you kids know how important you think reading is.
Perhaps enlist their help in a book drive for your classroom in the community or through your PTO.
Best of luck!

Not sure if this would work for your school district population but I always ask my students to bring (on the first day of school) a fiction and non-fiction book from home. I realize this suggestion is a minimillisticl solution to the bigger problems… NO books in your classroom. Good luck! Enjoy teaching!

Retired teachers often want to get rid of their libraries - put an ad on kijiji.
Start up schools take a few years to get the many things in place. you do not have to have lots of in class resources.
Scholastic books have grade level teacher discount boxes in the summer ( usually June - maybe Aug) and they have several books at the grade 5/6 level but not all current. I did not like what was in the box, but it started my class library when I moved up from a lower grade.
if you use library books, then make sure you keep them in the class and track where they are ( who has what). You do not want to pay lost fees because a student took them home.
libraries often get rid of books - ask your local library how they get rid of books and if they would consider donating some of their discards to you. some discards are very good.
Garage sales

• there is a website that teachers sell stuff on - in Canada for other teachers - sorry I have not kept that info as my library is full.
  I usually go to Chapters/indigo and buy my summer reading of 8-20 books for the summer. usually I find more current books than Scholastic and those books I choose and Like come out in about a year in Scholastic. In Canada, save your receipts and get a signature from a school admin person to use for out $1000 tax benefit that is coming into affect that we can use in our tax.
  The other ideas about students bringing books from home is great if you are in a community that has books at home. I have worked in some schools where students have no books at home.
  Depending on the size of community, contact a service club like the Elks, the Lions, the Kinettes, or a church group or local businessman (successful business in your area) and see if they would donate $500 or ??? To books.
  I have asked people from my church for various amounts of money for: after school care for a student whose parents dropped off at 6 am and picked up at 5 pm even in winter ( yes -30degrees C), technology, and stuff for my class. if you have the confidence to ask and explain graciously, I have not been refused.
  You could subscribe to learning a-z and use their on line books.
  libraries have access to lots of free reading books and resources.
  good luck.