Transferring backwards from Gen 5 to Gen 4

[beachgoth]

I have a general question, is there any way to transfer Pokémon from gen 5 back to gen 4? I'm currently working on making living dex for my games, before I found out about PkHex I transferred my gen 3 and 4 Pokémon up to gen 5. Is there any way to transfer these Pokémon back or would it be easier to start a new save file?

[BlackShark]

Go to Settings > Advanced and allow incompatible conversions.