If $$\frac{a}{b} = \frac{1}{2},$$   find the value of the expression $$\frac{{\left( {2a - 5b} \right)}}{{\left( {5a + 3b} \right)}}$$   = ?

$$\eqalign{ & \frac{a}{b} = \frac{1}{2} \cr & {\text{Let }}a = x,{\text{ }}b = 2x \cr & {\text{Then,}}\frac{{\left( {2a - 5b} \right)}}{{\left( {5a + 3b} \right)}} \cr & = \frac{{2x - 10x}}{{5x + 6x}} \cr & {\text{ = }}\frac{{ - 8x}}{{11x}} \cr & = \frac{{ - 8}}{{11}} \cr} $$