Can you trade from Pokémon Black/White to Pokémon HeartGold/SoulSilver
I want to trade from generation 5 to 4 is this possible?
It isn't.
The only time it's been possible to transfer Pokemon back to a previous generation was way back in gen 2 where they could potentially be sent back to gen 1. From gen 3 to gen 4 onward any transfers of Pokemon to newer generations have been permanent including those done through that silly archery minigame thing you use to move them from gen 4 games to gen 5.