The zeroes can be expressed as x=⅕, that is, x-⅕=0, 5x-1=0; and x=-5, that is, x+5=0. The multiplicity factor means that the factor is (5x-1)².
So, f(x)=(5x-1)²(x+5)=(25x²-10x+1)(x+5)=
25x³-10x²+ x+
125x²-50x+5=25x³+115x²-49x+5.
This is one example of the required function. Multiplying this polynomial by a constant gives other examples.