list manipulation - Understanding `NestList` with multiple functions

For a function f[n, a], where a is a list and n is a whole number, what is the correct syntax for

f[n - 5, f[n - 4, f[n - 3, f[n - 2, f[n - 1, f[n, a]]]]]]

All I want to do is

fg[n_, w_] := f1@ff[n, w]
fg[n - 2, fg[n - 1, fg[n, list]]]

as shown above, which works, but I am having to manually write out n-3,n-2,n-1,...

Have tried

fg[n_][w_] := f1@ff[n, w]
NestList[fg[n], list, 3]

but doesn't quite work. I think it needs a #-1 in there somewhere, that is applied to the n, but not sure on syntax.

Answer

Last @ Nest[{ #[[1]] - 1,  f1[ ff[ #[[1]], #[[2]] ] ] } &,
            {n, list}, 
            3]

f1[ff[-2 + n, f1[ff[-1 + n, f1[ff[n, list]]]]]]

Comments

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