We hear what you're saying. We see your point of view. We feel your pain. Also, you smell bad and possibly taste funny, the latter of which we don't intend to test.
But if you believe these are the only five ways you can detect information about your environment or alterations to your person, we're going to punch you in the face. There. Boom. You will feel it thanks to nociception, the ability to sense pain.
There are lots more, too, although the lists vary and the final number-of-senses tally is in great dispute. There are several boring ones that your body does without you knowing it. So let's skip those. More interesting is proprioception, which helps you pass the "close your eyes and touch your nose" test. Basically, it's what lets two parts of your body connect without visual confirmation. If you're (successfully) rubbing your eyes in disbelief, you used proprioception to do it. If you accidently smacked yourself in the forehead instead, you experienced a proprioception fail.
Apart from those, hunger and thirst can count according to some, as can feelings of hot and cold. Itch, interestingly, is apparently independent from both touch and pain. It's annoying on so many levels!
Author's Note: 10 Completely False ‘Facts’ Everyone Knows
This article was pretty cool to research and write. I came away with a sense (Ha! Did you see what I did there?!) that many of these "facts" are just things we take for granted without giving them much thought. But that if we did give them more thought, we could probably reach most of these conclusions on our own. However, thanks to me, you have now given them more thought but without having to bother with coming to the correct conclusions all by yourself. You're welcome.
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