What is an irrational number between 5.2 and 5.5

To answer this question let us first define what a rational and irrational number is. A rational number is basically a number whose decimals are terminating (ie have an end) or repeating (continuously repeats the same pattern. 
An example of this from your question would be 
5.3 - terminating rational number5.333333333333 - repeating rational number

Answer is negative 2