\[\left( 5a^{2} - 2a - 3 \right) - \left( 2a^{2} + 2a - 5 \right) =\]
\[= 5a^{2} - 2a - 3 - 2a^{2} - 2a + 5 =\]
\[= 3a^{2} - 4a + 2.\]