Let 5 - √3 be rational,

Then, 5 - √3 can be expressed as where, p and q are co-prime integers and

q ≠ 0,

we have,

As p and q are integers, 5q - p is also an integer

is a rational number.

But √3 is an irrational number, so the equality is not possible.

This contradicts our assumption, that 5 - √3 is a rational number.

Therefore, 5 - √3 is an irrational number.