I think you need to flip the problem upside down. Rather than you being the one to say which of their toys should go to recycling, have them decide. The process will be better accepted by your 5-year-olds if it is a choice that they make themselves. Set the scene for the project by doing the following:
Get a new simple storage solution, as suggested in the KonMari method. Kids are usually interested in new things.
Before you fill up the new storage...
Put out 3 cardboard boxes
- One labeled "give to kids in need"
- One labeled "trash"
- One labeled "keep and put in new storage system"
Avoid suggesting or pre-sorting their toys for them. This will feel like you are taking their things away. Have them come with you to the donation center, so they understand where it goes. Repeat the sorting exercise every couple of months. If they are still reluctant to put anything in the give away / trash boxes, you can introduce the idea of "do you love this e.g. teddy bear? does it make you happy?"
Edit: one thing I forgot to say... with my husband who is reluctant to let go of things, I tell him that we'll keep the "give away" bag in the basement for a couple weeks in case he changes his mind. That way, if regrets set in, it's not such a forever decision.