My main problem is that I dont know write this polynomial's function.
There are three turning points, so you have a fourth order polynomial. It has roots at -5 and -1 (i..e. places where the function is zero.
Write the function as f(x) = -(x + 5)(x + 1)(x - a)(x - b) where a and b are to be found (the initial negative sign is because the function goes to -infinity as x goes to +/- infinity)
When x = 0 we have f(0) = -25, so -5*a*b = -25 ...(1)
There gradient of f is zero when x = -3, so differentiate f with respect to x and set the result equal to zero (with x = -3)
df/dx = -(4*x^3 + (18-3a-3b)*x^2 + (2ab-12a-12b+10)*x - 6ab - 5a -5b)
so 4*(-3)^3 + (18 - 3a - 3b)*(-3)^2 + (2ab -12a -12b + 10)*(-3) -6ab - 5a -5b = 0 ...(2)
You now have two equations for the two unknowns a and b.
Can you take it from here?