The very notion of "base tastes" is confusing. It's not like you can decompose every taste into just these 5 base tastes, i.e. a strawberry taste. Yes, they are omnipresent and prominent, but why single them out?
When you see a chair or a lake, no matter how different those things are, the sensory mechanism is the same and quite limited in a way.
It's also like language, or arabic numerals. You can express any number or any idea, to infinity, but they are all composed out of a tiny alphabet of only 10 digits or 26 letters.
And it's not some desire to reduce or deconstruct anything, because anyone just hates calling a strawberry a strawberry for some reason. It's simply what actually IS. Our perception of the taste of strawberry, and everything else, IS composed of only a few "base tastes". You don't have a whole sensor cell just for strawberries, and an infinite number of others for the infinite number of other things. You have a few senor types which are general purpose, and can compose a perception for strawberry, or anything else, even if strawberries were invented today and none of your evolutionary history never encountered a strawberry before.
Which is why food tastes very different if you lose your sense of smell, and why making artificial flavours is not just a matter of mixing a few base flavours.
Yes when we eat something we are experiencing more than just tatse, but so what? The fact that our full perception of a strawberry includes smell is as irrelevant to the validity of the concept of "a few base tastes" as the fact that it also includes sight and texture and memories of that summer job you had picking strawberries one year when you were 12.
There is no Van Gogh sensor gene in your retina. There are just a very few types of light sensor, which all sight is composed of. Taste is the same. Smell is the same. Smell just has a bit larger alphabet, but it's still finite. The original comment questioned the validity of the very idea that there was any such finite alphabet. There is no possible question about that.