How many senses does the average human have? If you equate senses with their receptors, such as the retinas in your eyes and the cochlea in your ears, then the traditional answer to this question is five: sight, hearing, touch, smell, and taste. These are called the "exteroceptive" senses because they carry information about the external world.
But your body also has receptors for events occurring inside you, such as your beating heart, expanding lungs, gurgling stomach, and many other movements that you're completely unaware of. These are traditionally grouped together as another sense, called "interoception."
Yet a proper answer to this question is even more complex and interesting. For one thing, your body has receptors to carry other types of information, such as temperature, that we don't usually consider to be senses.
Also, some of your receptors are used for more than one sense. Your retinas, for example, are portals for the light waves you need for vision, but some retinal cells also inform your brain if it's daytime or nighttime. This unnamed "day/night sense" is the basis for circadian rhythms that affect your metabolism and your sleep/wake cycle.
Your brain also constructs senses that you don't have receptors for. Examples are flavour, which the brain constructs from gustatory (taste) and olfactory (smell) data, and wetness, which is created from touch and temperature.
Your brain appears to predict what you might see before you see it, based on past experience, the state of your body, and your current situation. It seems to combine those predictions with the incoming sense data from your retinas to construct your visual experience of the world around you.
Similarly, when you place your fingers on your wrist to feel your pulse, you're likely feeling a construction based on your brain's predictions and the actual sense data. You don't experience sensations only with your sense organs. Your brain does a great deal of the work.