Do you use the plastic buckets for purposes other than organizing your bricks?
Well the buckets themselves have value.
If you can't use them you could sell them to people who want them.

Your example set #5560 has an original box only listing on BrickLink, as do many other of the brick boxes, run a search for "brick box" you'll find lots.

The prices vary from a few dollars, to ~$20 for you example. They don't seem to be big sellers, but there are some sales.

If you have a lot of them and/or you want them gone quicker set up an eBay listing for all of them.