**Solution:**

Let us assume, to the contrary that 4 - 5√2 is rational.

So, we can find coprime integers a and b(b ≠ 0)

such that 4 - 5√2 = a/b

=> 5√2 = 4 - a/b

=> √2 = (4b - a)/5b

Since a and b are integers, (4b - a)/5b is rational.

So, √2 is rational.

But this contradicts the fact that √2 is irrational.

**Hence, 4 - 5√2 is irrational.**