It is often reported that "five-0" is slang for "the police" but this usage post-dates the original 1970s version of the series and is probably derived from the show rather than the other way round. In the show "five-0" is the name of the police unit and was created by the original writers, almost certainly as a reference to Hawaii being the 50th state of the USA.
He is a bit of a mysterious character for the show. In the first season he was established to have been a senior US Navy commissioned officer who'd served as Steve McGarrett's commanding officer during Steve's time as a navy seal. Joe White is very shrewd, intelligent and with a no nonsense take no prisoners
type of attitude and approach to life. As a senior officer at the rank of captain we can presume that he's seen combat in the gulf war and operation Iraqi freedom along with some "highly classified, clandestine
military missions of the top secret nature. Besides his seal background Joe White most likely has loyal
contacts in the CIA, DOD, NSC and other federal agencies which he won't discuss not even with Steve McGarrett. It is also interesting to note that actor Terry O'Quinn also portrayed a career naval officer in the CBS series JAG for many episodes. As Admiral Thomas Boone, a decorated naval aviator and Vietnam veteran who was a close friend and confidante of JAG's boss, Admiral Jethro Chegwidden. Both admirals served together for many years and knew each other quite well and the character of Boone was similar to Joe White though not quite as mysterious and quite a bit more likeable.