Manipulate mapping on lists

For some function f, consider the following expression:

 f[2] f[5] - f[1] f[2] f[5] - f[2] f[3] f[5] + f[1] f[2] f[3] f[5] - f[2] f[4] f[5] + f[1] f[2] f[4] f[5] + f[2] f[3] f[4] f[5] - f[1] f[2] f[3] f[4] f[5]

How can I manipulate this expression so that it instead reads:

f[2,5] - f[1,2,5] - f[2,3,5] + f[1,2,3,5] - f[2,4,5] + f[1,2,4,5] + f[2,3,4,5] - f[1,2,3,4,5]

I.e. the function is now implemented on a list of the individual arguments. I’ve had a go at trying Map to achieve this but with no luck.

EDIT TO QUESTION

To make this more meaningful for functions, how can the above string be passed as a single vector. Specifically, how can we obtain the output

f[{2,5}] - f[{1,2,5}] - f[{2,3,5}] + f[{1,2,3,5}] - f[{2,4,5}] + f[{1,2,4,5}] + f[{2,3,4,5}] - f[{1,2,3,4,5}],

this form can then be applied to a predefined function f[u] that operates on the list u. The function should also be able to take additional arguments.

Times[f[x__], f[y__]] ^:= f[x, y]

expr //. Times[f[x__], f[y__]] :> f[x, y]