Put the roots on line(x-axis), check if an interval is positive or negative by substituting i.e: x=-4 {(-infinite, -3)} to (x+3)^5 (x-1)(x-4)^2,

if (x+3)^5 (x-1)(x-4)^2 positive the sing is + else -

At the end of process you will get your roots on line(x-axis)and sing in witch interval.

(x+3)^5 (x-1)(x-4)^2 < 0

so you take all intervals with sing minus.