Given that $\Bbb R$ denotes the set of all real numbers, $\Bbb Z$ the set of all intergers, and $\Bbb Z^-$ the set of all negative integers, describe each of the following sets.
a. $\{x\in\Bbb R \mid -5<x<1\}$
b. $\{x\in\Bbb Z \mid -5<x<1\}$
c. $\{x\in\Bbb Z^- \mid -5<x<1\}$
When using set builder notation like this, you have something like:
$$\{x\in A~|~\text{statement involving } x\}$$
and this is read to mean "The set of all elements from $A$ such that they satisfy the statement."
Your first, $\{x\in\Bbb R~|~-5<x<1\}$ is then "The set of all real numbers which are strictly between $-5$ and $1$. Something called an open interval. Your set would also commonly be denoted using interval notation as $(-5,1)$ meaning the same thing.
The remaining sets in your question are read identically, with the only difference being rather than looking at the set of all real numbers in the range, we are only looking at numbers from the set of negative integers or the integers. You can see that there will only be a handful of such numbers in each.
The biggest thing to remember about the differences between these two is that $0$ is not negative.