(Leftover post from Friday)
Found an official page of MI5 Myths, on their website:
We [MI5] are a civilian organisation and members of staff have no executive powers, such as the authority to detain or arrest people. We are not a "secret police force."
So there you have it. MI5 is not to be confused with the Secret Intelligence Service (sometimes called called MI6, who don't have a website I could find) or Government Communications Headquarters (GCHQ). MI5 don't assassinate people, or illegally eavesdrop communications, and they will hire people over 5ft 11. The site also has a glossary that's quite useful. Taxpayer's money at work.