So far as I'm aware, "spicy" is not one of the 5 main flavors, but "salty" is. Spiciness and the coolness of menthol are separate, as they have nothing to do with taste and everything to do with triggering heat/cold detection - they just work particularly well on the mucous membranes in your mouth.
Also this reminds me a lot of that other WG VN where you are hired as the head chef and have to do a rhythm minigame and you can make the sassy maid that is the tutorial boss embarrassed at how much you made her eat. I can't find it now, though, and I forget what it was called.