Hey there!
The answer to your question is z > -4
We can solve this like it is an equation, with one exception. When you divide or multiply by a negative number, in an inequality, you have to flip the inequality sign.
-2z - 3 < 5 add 3 to both sides
-2z < 8 divide both sides by -2, and flip the inequality sign
z > -4
Good luck! Hope it helps, and have a great day!