Override Cart Item Price

It sounds like you may want to add a coupon for $5 off that you only give to nonprofit organizations. Here’s how to create a coupon:

https://docs.woocommerce.com/document/coupon-management/#section-1

If you just want something like a checkbox during the purchase process, Product Add-Ons can do this:

https://woocommerce.com/products/product-add-ons/

Screenshot of an example configuration:

https://adam-a8c.d.pr/5xNLCC

Result on the product page:

https://adam-a8c.d.pr/VHwWPb

Of course, there’s no built in way to determine if someone is really a non-profit or not, so a coupon that you only give out as needed seems like the best way.