Arthur tells you that he is thinking of an irrational number between 4 and 5, and he wants to guess what it is one possibility you could guess is?

Almost all real numbers between 4 and 5 are irrational, so just pick any two of those real numbers.

You can also try this

square 4 and 5 and the result is 16 and 25 and take any number between 16 and 25 and square root it and the result will not only lie between 4 and 5 but also irrational and real at the same time

One of the irrational number between 4 and 5 is 3+sqrt2