\[\left( 5\frac{1}{4} - 5\frac{1}{2} \right)^{3} = \left( \frac{21}{4} - \frac{11^{\backslash 3}}{2} \right)^{3} =\]
\[= \left( \frac{21}{4} - \frac{22}{4} \right)^{3} = \left( - \frac{1}{4} \right)^{3} =\]
\[= - \left( \frac{1}{4} \right)^{3} = - \frac{1}{4^{3}} = - \frac{1}{64}\]