There's no clear origin for this phrase. It's meaning seems to be that there are multiple options to follow to arrive at the same conclusion. ( source )

The first mention of the term 'sixth sense' occurred in 1712, in William Whitson’s Primitive Christianity Reviv’d, Volume V: ”Then said Peter, That is false; for there is a sixth Sense, that of Prescience: for the other five Senses are capable only of Knowledg; but the Sixth of Foreknowledg; which Sense the Prophets had.” ( source ) And how we use it today is not different from Whitson's observation. Sixth sense is indeed a foreknowledge of sorts - your gut instincts.