$x^{x^5} = 5$

We note that the possible value of $x$ is $\sqrt[5]{5}$ , so that the equation $x^{x^{5}} = 5$ fulfilled.

Then, we have $x^{20} = ( \sqrt[5]{5} ) ^{20} = 5^{4} = \boxed{625}.$

Hope you all can understand it

Observe that if $x^5 = 5$ , then we can rewrite $x^5$ as

$x^5 = x^{x^5} = 5$

$x^{20} = (x^5)^4 = 5^4 = 625$