To do these types of problems fast, I highly recommend you learn synthetic division-it helped me so much in Algebra II class.
It is kind of hard to explain on here, so I recommend searching synthetic division on you tube.
Anyway, by doing that you get (x-5) as a zero and are left with 6x^2 -x -1, which you can plug in the quadratic formula, and you get x= -1/3 and x=1/2
Hope, this tip helps you get started, but if not another tip would be (although it takes much more time) to just start dividing the polynomial by numbers like: x= (+/-) 6,1,2,3,5 because these numbers are factors of 5 or 6.