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\begin{aligned} x^{3}-5 x^{2}-x+5 &=0 & & \text { Factor by grouping. } \\ x^{2}(x-5)-(x-5) &=0 & & \text { Factor out the common factor. } \\ \left(x^{2}-1\right)(x-5) &=0 & & \text { Factor the difference of squares. } \\ (x+1)(x-1)(x-5) &=0 & & \text { Set each factor equal to zero. } \end{aligned}