Question

find one irrational number between 5 and 6

Answer 1

a number which is non terminating and non recurring is known as irrational number 
there are uncountable irrational numbers between 5 and 6 
5.435782957393845755..................... 
5.9934735896347457369309563846... 
etc etc

Answer 2

5.01001000100001.......

And you just keep adding an extra zero every time to make a non repeating series