You could say there are 5 major categories of external senses, technically exteroceptors, and many subcategories. Touch, for example, technically somatosensory, could be subdivided into pressure, vibration, light touch, tickle, itch, temperature, pain, kinesthesia, etc. Then there are other numerous internal senses, technically interoceptors, such as hunger, the vestibular and proprioception systems, etc.

In any case, once nerves are successfuly intercepted for send and receive operations, all this information becomes nothing more than electrical signals, so even if we had thousands of senses, it does not seem to be an obstacle to the generation of a convincing reality. You could just plug an AI world generator to send signals through your nerves and fully emulate an entire reality, from vision and touch, to balance and speed.

Correct me if I am wrong, but everything we feel is either an electrical signal coming from a nerve and interpreted by the brain, or a chemical interacting directly with receptors in the brain.