Write five rational numbers greater than -2.

Hint: Rational numbers are categorized as all numbers except irrational numbers. So, by virtue of this definition we proceed to solve our problem regarding writing rational numbers with the given condition that they must be greater than -2.

Complete step-by-step answer:
In mathematics, the number system is the branch that deals with various types of numbers possible to form and easy to operate with different operators such as addition, multiplication and so on.
Four major types of numbers can be classified as:

Natural numbers, whole numbers, integers, and rational numbers. Irrational numbers come under the category of imaginary numbers.

So, rational numbers are those numbers which can be represented in the form of $\dfrac{p}{q}$, where p is the numerator and q is the denominator. P and Q may belong to any of the three categories such as natural, whole or integers. So, rational numbers are the biggest set containing other subsets of natural numbers, whole numbers and integers.

Rational numbers can also be expressed in the decimal number system. For example, $\dfrac{2}{5}$ which is a rational number can also be simplified as $0.4$.

In our problem, we are required to find five rational numbers greater than -2.

So, these number may be:
First number: $\dfrac{2}{5}$.
Second number: $\dfrac{11}{13}$.
Third number: $0$.
Fourth number: $\dfrac{34}{7}=4\dfrac{6}{7}$.
Fifth number: $2.4$.

Therefore, five rational numbers greater than -2 are $\dfrac{2}{5},\dfrac{11}{13},0,4\dfrac{6}{7},2.4$.

Note: The key step in solving this problem is the knowledge of the rational number system and different ways of representation of rational number. The knowledge of various kinds of number systems is essential and very important in further studies of mathematics.