Let us assume that (5 – 2√3) is a rational.
Subtract given number form 5, considering 5 is a rational number.
As we know, Difference of two rational numbers is a rational.
5 – (5 – 2√3) is rational
2√3 is rational
Which is only possible if 2 is rational and √3 is rational
As we know, product of two rational number is rational.
But the fact is √3 is an irrational.
Which is contradict to our assumption.
(5 – 2√3) is an irrational number.