Hi! Does it make sense to put them into the folder: sprites/pokemon/versions/generation-v/black-and-white/icons/animated/ ?

Now you put them in: sprites/pokemon/versions/generation-v/animated-icons/

I'd argue the following makes more sense as it matches the structure of generation-vii and viii (albeit they do not include animated icons).
-\ generation-v
----\ black-and-white
----\ icons
-------\animated

Rather than the proposed:
-\ generation-v
----\ black-and-white
----\ icons
-------\animated

I have updated the PR to match the first option, but if requested I can have it match the second.

Alright, let's go with the proposed nesting. Could you remove all the leading 0 from the filenames?

Leading zeros have been removed!