How to find the zeros of a polynomial function degree 5?

Begin by trying to see which values would allow the function to become zero. 

Try x=1, x=-1, x=0 and see if this works. 

Let's say that x=1 gives f(x)=0 <-- the given function with degree of 5 

You can say; 

ax⁵+bx⁴+cx³+dx²+ex+f=(x-1)(Ax⁴+Bx³+Cx²+Dx-f) <-- rewrite variables with 1 less degree. Solve by expanding. 

If, you find that numbers such as x=1, x=-1, x=0 or any others don't work out, it might be best to find a set of zeros from a calculator and basing your calculations on that. 

Hope I helped :)