\[\left( \frac{5}{12} \right)^{2} - \left( \frac{3}{4} \right)^{2} = \left( \frac{5}{12} \right)^{2} - \left( \frac{9}{12} \right)^{2} =\]
\[= \left( \frac{5}{12} - \frac{9}{12} \right)\left( \frac{5}{12} + \frac{9}{12} \right) =\]
\[= - \frac{4}{12} \cdot \frac{14}{12} = - \frac{7}{3 \cdot 6} = - \frac{7}{18}.\]