Ice's Salad Function

Ice's Salad Function is one of the worst functions ever created.

$$f(x)$$ would be $$\left(x^{x!}\right)\uparrow\uparrow x$$ (or $$\underbrace \left(x^{x!}\right)_x $$, both ways are correct).

$$f(1)$$(1^1!) would simply be 1.

$$f(2)$$ (2^2^2^2) would be 65536.

$$f(3)$$ (3^6^3^6^3^6) would be a number greater than what most computers can handle.

$$f(4)$$ would be 4^24^4^24^4^24^4^24.

$$f(5)$$ would be 5^120^5^120^5^120^5^120^5^120, and so on.

Extensions
$$f(x,y)$$ would be $$\left(x+y^{x+y!}\right)\uparrow\uparrow x+y$$