how did you find out about the local school throwing away 50+ small dell quad-core i5s?
Hard to give more info, there isn’t just one auction site for all schools or counties, but a bit of googling will probably get you what you want.
On the other hand, you're often looking at "Lot of 38 Dell Latitude 5570 Core i7", "These items have been used by students or employees within a professional Community College environment. Items have been maintained, updated, and well kept.", minimum bid $5,800.00
Or something like "(1) Dell Optiplex 780, bad power supply, pickup in-person only, we don't ship" so you'd have to be in the area and interested in swapping a PSU.