In determining the factorization, it is a good trick to know that when the coefficient of the x^2 is indeed one (as it is in this case), solving for the two factors is much easier.
Basically, what two numbers, when multiplied, equal positive 5, but when added together, equal negative 6?
The only possibility is -1 and -5. Therefore (x-1), (x-5)
To check your answer, you can use the FOIL method of multiplying your two factors (first, outside, inside, last), to arrive back to the original equation:
First = x times x equals x^2.
Outside = x times -5 equals -5x.
Inside = -1 times x equals -x.
Last = -1 times -5 equals 5.
Combined then you have x^2 -5x -x +5, simplified to x^2-6x+5.