The council most often associated with rejecting the pre-existence of souls was the Second Council of Constantinople in 553, which condemned Origen and several of his teachings, including the idea of souls existing before birth.
What it was about
Origen’s view was not just that souls were spiritual in nature, but that they existed before their bodily lives. That teaching was among the ideas later anathematized in the controversy settled at Constantinople in 553.
Why the answer can vary
Some people loosely refer to this as the “Fifth Ecumenical Council,” which is another name for the Second Council of Constantinople. In some discussions, related but different councils are mentioned because later theology also dealt with the soul, but the clearest historical match for rejecting pre-existent souls is this council.
In plain terms
If someone asks which council went against the prior existence of souls, the best direct answer is: the Second Council of Constantinople in 553.