$=\frac{(5-2i)(4-2i)}{(4+2i)(4-2i)}$
Simplify $\frac{(5-2i)(4-2i)}{(4+2i)(4-2i)}:{\quad}\frac{16-18i}{20}$$=\frac{16-18i}{20}$
Apply the fraction rule $\frac{a+bi}{c}=\frac{a}{c}+\frac{b}{c}i$$=\frac{16}{20}+\frac{-18}{20}i$
Simplify $\frac{16}{20}+\frac{-18}{20}i:{\quad}\frac{4}{5}-\frac{9}{10}i$$=\frac{4}{5}-\frac{9}{10}i$