In traditional Western culture, for a long time there have been only four basic tastes: sweet, sour, salty, and bitter. The fifth taste, umami or "savory," was discovered and added to the list quite recently; the compounds were isolated in Japan in 1908 and the specific taste receptors discovered only in 2002 (Oxford Academic).
From a scientific standpoint, there are five distinct tastes that can be perceived by your taste buds:
There is also a current debate about the taste of fat, and the potential discovery of taste receptors that can specifically sense lipids and fatty acids, which would give us six distinct tastes, scientifically speaking (Scientific American).
These are scientifically classified as tastes precisely because of the way they are detected by taste receptors on your tongue. There are other sensations that the tongue can detect by other means, generally by the somatosensory nervous system. These include a wide variety of other flavors or "mouth-feels," including:
- Pungency (your "hot" or "spicy" flavor)
- Coolness (Perceived cold from thing such as peppermint and menthol)
- Astrigency (mouth puckering from tea, red wine, rhubarb, etc)
- Heartiness ("full flavor" or kokumi, found in things like garlic to enhance other flavors without a flavor of its own) (Food Proteins and Peptides)
There are other less scientific ways of defining the tastes; notably, traditional Hindu Ayurvedic medicine (or simply Ayurveda) recognizes six tastes as:
Given the phrasing of your original question, perhaps that is what you are thinking of.