so that would be:Assuming the third term ought to be

if you had a typo on the 4th term also, (+16 instead of -16)

you would have a polynomial which has 3 factors (some repeated)

and 3 different integer roots for f(x) = 0.

x^5 - 6x^4 + 5x^3 + 16x^2 - 12x - 16

The factors of the first three terms are:

(x^3)(x - 5)(x - 1)

I can't factorise the last three terms