Answer
$$\overline x = - \frac{4}{3}$$
Work Step by Step
$$\eqalign{
& {m_1} = 7,{\text{ }}{m_2} = 3,{\text{ }}{m_3} = 5 \cr
& {\text{Located at }} \cr
& {x_1} = - 5,{\text{ }}{x_2} = 0,{x_3} = 3 \cr
& {\text{The moment about the origin is }} \cr
& {M_0} = {m_1}{x_1} + {m_2}{x_2} + {m_3}{x_3} \cr
& {M_0} = \left( 7 \right)\left( { - 5} \right) + \left( 3 \right)\left( 0 \right) + \left( 5 \right)\left( 3 \right) \cr
& {M_0} = - 20 \cr
& m{\text{ is the total mass of the system}} \cr
& m = {m_1} + {m_2} + {m_3} \cr
& m = 7 + 3 + 5 \cr
& m = 15 \cr
& {\text{The center of mass is }}\overline x = \frac{{{M_0}}}{m}{\text{, then}} \cr
& \overline x = - \frac{{20}}{{15}} \cr
& \overline x = - \frac{4}{3} \cr} $$
