I also take issue with the idea that there are just five cardinal flavors. There are many, many more, which cannot be expressed in terms of these five, especially in the savory category.
Think of the flavor of meat, spices, and pepper. They are all fundamentally different, and yet would be bundled under savory in the 5-flavor scheme. The word "spicy" itself has two distinct meanings.
The five flavors model is an outdated model of what taste buds detect, a sixth has been established (oleogustus, associated with fatty acids and particularly with rancidity.) Furthermore, while not technically “tastes” in the detected-by-tastebuds sende, unctuousness (the mouthfeel of fats) and spiciness (detected by pain receptors instead of tastebuds) are part of what most people mean when they talk about “taste”.
Some such substances occur across a broad range of foods, or in varieties that differ from each other in ways that don't really matter to your digestive system, and you can pick them up and consider them to be a flavor common to those foods.
Some are unique. You can pick those up too.
In either case, your perception of the same taste will vary according to the current state of your nutrition. Steven Callahan noted that, when he was lost at sea and food was scarce, fish eyes tasted significantly better than the rest of the fish. That is because they contain important nutrients, which your tongue can detect, but which you don't ordinarily care about. You start to care as you develop deficiencies.
A model of a small number of "basic flavors" doesn't even allow for this phenomenon to exist. It is fundamentally misguided.