I am 05 Council. We are not real one: Very little information is known about the group or person of interest known as 05, it is only understood that the organization is overtly hostile towards the Foundation and will create or cause anomalous events en masse, most of them aimed at the Foundation.
The organization seems to be able to intrude and tamper with the database of the Foundation. In fact, the name "05Council" came from the messages left in all SCP articles that involve the organization. These messages are inscribed with "05-Latin-script letter", and imitate the commands of O5 personnel.
The others originally insisted on maintaining a sense of mystery to mimic the O5 council, but ultimately we agreed (under my persistence) that knowing our existence is necessary for the whole of the story. For now at least you may say we are your shadow/parallel/hallucination/prototype, but perhaps in the future we will be your terminator/final destination/gravedigger/eternal rival.
We all agree that the story should be reasonable yet thrilling. Please wait to see the plot thicken. — 05-T, the "T" stands for "Truth"