list the elements in sets.

hey guys having problems with this question.

List the elements in the following sets:

**1.** $\displaystyle \{ x \epsilon \mathbb{N} : x^2 < 23\}$

**My Answer:**

Elements x = 1,2,3,4

**2.** $\displaystyle \{ x \epsilon \mathbb{Z} : x^2 < 23\}$

**My Answer:**

Elements x = -4,-3,-2,0,1,2,3,4

**3.** $\displaystyle \{ x \epsilon \mathbb{R} : x^3 + 5x\}$

**My Answer:**

$\displaystyle \Rightarrow x^3 + 5x = 0$

$\displaystyle \Rightarrow x(x^2 + 5) = 0$

so I know $\displaystyle x = 0$, but dont know how to find $\displaystyle x$ from $\displaystyle x^2 + 5 = 0$

**4.** $\displaystyle \{ x \epsilon \mathbb{Q} : x^2 + 4 = 7\}$

**My Answer:**

I know Q is rational numbers but dont know how to find this one.

**5.** $\displaystyle \{ \}$

**My Answer:**

This is just an empty set so would it be elements: $\displaystyle \emptyset$ ?

Any help with these 5 questions would be much appreciated.