How many senses even a human can be said to have is a matter of definition, although it's generally agreed to be more than five. An extreme way of counting would be to consider every specific type of sensory cell as representing one 'sense'. This, however, results in the conclusion that vision is four separate senses: one for black-and-white (the rod cells) and one each for the primary colours (the cone cells). This, it's probably fair to say, is not something that's widely considered helpful - although it may well be useful to neurobiologists.
If we don't go that far, then, we can still consider vision, hearing, taste, and smell to be singular senses. It is, however, not uncommon to consider the ability to sense temperature as distinct from the ability to sense that you are physically touching something. Pain can also be considered a distinct sense, since you can obviously 'feel' when you have, say, a headache, but it's hard to argue that that should count as 'touch'.
