Multiply both sides by 3:

$\displaystyle\frac{{-{2}{z}-{3}}}{{3}}\cdot{3}<{5}\cdot{3}\usepackage{cmbright}\Huge\$ or $\displaystyle-{2}{z}-{3}<{15}\usepackage{cmbright}\Huge\$

Add 3 to both sides:

$\displaystyle-{2}{z}-{3}+{3}<{15}+{3}\usepackage{cmbright}\Huge\$ or $\displaystyle-{2}{z}<{18}\usepackage{cmbright}\Huge\$

Divide both sides by $\displaystyle-{2}\usepackage{cmbright}\Huge\$ and reverse the inequality symbol:

$\displaystyle\frac{{-{2}{z}}}{{-{{2}}}}>\frac{{18}}{{-{{2}}}}\usepackage{cmbright}\Huge\$ or $\displaystyle{z}>-{9}\usepackage{cmbright}\Huge\$