You may have mixed up the x-value and y-value when substituting them into the equation.

$\displaystyle{4}{\left(-{5}\right)}-{2}{\left(-{2}\right)}={2}\usepackage{cmbright}\Huge\$ or $\displaystyle-{20}+{4}={2}\usepackage{cmbright}\Huge\$ or $\displaystyle-{16}={2}\usepackage{cmbright}\Huge\$

This is not a true statement, so the ordered pair $\displaystyle{\left(-{2},-{5}\right)}\usepackage{cmbright}\Huge\$ is not a solution to the equation.