You got your sweet, salty, sour, bitter and umami.
Well, at my house we've been cooking with a sixth taste, burny. Not smoky, though there was a bit of that in the stock we used for this soup.
The smoky came from barbecued pork rib bones. They were simmered with turkey leftovers from Thanksgiving.
The burny, though. It's easy, it's free, it's natural. And it tastes good.
Just throw your chopped vegetables into a pan with hot grease and cook until brown corners appear. It doesn't compromise the native flavor of the vegetables at all; just adds a zing of caramelization. And if you brown until black corners appear, you get that special sixth taste. A little touch of carbon.
Why not? I know in England they make gravy from burnt onions if there's no meat. Which I am going to try, now that I'm loving burny.