The polynomial of degree $5, P(x)$, has leading coefficient 1 , has roots of multiplicity 2 at $x=1$ and $x=0$, and a root of multiplicity 1 at $x=-5$. Find a possible formula for $P(x)$. \[ P(x)= \]

Step 1 ：The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-5.

Step 2 ：The roots of a polynomial are the values of x for which the polynomial equals zero. The multiplicity of a root is the number of times it appears as a root.

Step 3 ：The polynomial with leading coefficient 1 and roots r1, r2, ..., rn is given by P(x) = (x - r1)(x - r2)...(x - rn). The multiplicity of a root is represented by the power of its corresponding factor in the polynomial.

Step 4 ：So, in this case, the polynomial will be P(x) = (x - 1)^2 * (x - 0)^2 * (x - (-5))^1.

Step 5 ：By expanding and simplifying the above expression, we get the polynomial P(x) = x^5 + 3x^4 - 9x^3 + 5x^2.

Step 6 ：\(\boxed{P(x) = x^5 + 3x^4 - 9x^3 + 5x^2}\) is the possible formula for P(x).