"Proprioception" is different from touch. Our tactile sense is achieved through the nerve endings in our skin and throughout our body (the most fun parts of our body are the ones that have the highest density of nerve endings ;-). Our sense of balance and orientation comes from a different organ: our inner ear. This is what allows us to know whether we are upright or prostrate, without opening our eyes. None of the "traditional five" senses gives us this information. Only our inner ear can tell us that.

This is why people with vertigo think that the room is constantly spinning. It's an inner ear thing. Also, when astronauts experience weightlessness, this sense becomes utterly useless. It takes some time to get used to being without this sense. Most astronauts vomit the first time they enter orbit.

So I would call proproiception/balance a sixth sense.