1. **Stating the problem:** Solve the quadratic equation $$x^{2} - 5x = 0$$. 2. **Rewrite the equation:** Factor out the common term $$x$$: $$x(x - 5) = 0$$. 3. **Use the zero product property:** For the product of two factors to be zero, at least one of the factors must be zero. 4. **Set each factor equal to zero:** - $$x = 0$$ - $$x - 5 = 0$$ 5. **Solve each equation:** - $$x = 0$$ - $$x = 5$$ 6. **Final answer:** The solutions to the equation are $$x = 0$$ and $$x = 5$$.