$$\frac{2^{-2}+5{\left({\displaystyle \frac{1}{2}}\right)}^0}{3-{\left({\displaystyle \frac{2}{3}}\right)}^{-2}}$$

$$=\frac{{\displaystyle \frac{1}{2^2}}+5·1}{3-{\left({\displaystyle \frac{3}{2}}\right)}^2}$$

$$=\frac{{\displaystyle \frac{1}{4}}+5}{3-{\displaystyle \frac{9}{4}}}$$

$$=\frac{{\displaystyle \frac{1}{4}}+{\displaystyle \frac{20}{4}}}{{\displaystyle \frac{12}{4}}-{\displaystyle \frac{9}{4}}}$$

$$=\frac{{\displaystyle \frac{21}{4}}}{{\displaystyle \frac{3}{4}}}$$

$$=\frac{{\displaystyle 21·4}}{{\displaystyle 4·3}}$$

$$=\frac{{\displaystyle 84}}{{\displaystyle 12}}$$