Scientists still aren't quite sure of exactly how many senses you have, or what even constitutes a sense, but you'd be hard-pressed to find one who believes you have five. Depending on how they count them, they usually wind up with something like 14 to 20. The five you learned about in school were just the five most evident senses, aka the boring ones you could have figured out for your own damn self. The rest are far more interesting.
Pictured: #19, smision.
The Harvard School of Medicine lists six extra ones that are pretty hard to argue against. Close your eyes, then touch your nose with your index finger. How did you know which one was your index finger without looking at it? How did you know where your nose was? Did you smell your finger to your nose? Did your sense of touch somehow tell you what the air molecules you encounter along the way to your nose feel like? Nah, that's proprioception, your body's awareness of where it is in relation to itself.
Oh, yeah. We just dropped the H-bomb on you.
Maybe the most interesting one they left out is your sense of timing, which might seem like it's only a sense in the way that fashion is a sense. But leading neurologists like David Eagleman think it's the most important of all the senses, since it's the thread that ties the rest of them together. An apple is just a series of different sensations without your sense of time telling you they're all happening at the same moment. Still not convinced? Try staring at a white wall in a totally silent room. Your sense of time tells you how much of your life has been wasted because you didn't take us at our word.
Good on you, fella.