Which of the binomials below is a factor of this trinomial? x^2-5x-36

The factors would be (x-9)(x+4).

You can use the decomposition method to find this. I personally use the chart method so I do not necessarily know how to explain the decomp method in detail. However the idea and end goal are the same for both of them.
Try to find what multiplys to the last part of the polynomial but will add to the middle part.
To check your work/factors you can try multiplying/foiling them out again to see if you get your original polynomial.