2√3 is an irrational number and subtraction of a rational number and an irrational number is an irrational number.

∴, 5 - 2√3 is irrational, where 2√3 is an irrational number while 5 is a rational number.

Alternative - Assume that 5 - 2√3 is rational
5 - 2√3 = a/b , where a and b are integers .
⇒ - 2√3 = a/b - 5
⇒ 2√3 = 5 - a/b
⇒ 2√3 = 5b/b - a/b
⇒ √3 = (5b – a) / 2b
we know that a, b, 2 and 5 are integers and they are also rational {i.e RHS is rational}
therefore √3 will be rational.
but we know that √3 is irrational.
there is a contradiction
so, 5 - 2√3 is an irrational number