Because $\displaystyle x^{\frac{1}{4}} = - 5$ is impossible the there is one solution.
$\displaystyle x^{\frac{1}{4}} = 4\quad \Rightarrow \quad x = 64$
Plato made a simple careless mistake. Be that as it may, it's a mere detail - it's the method that's important and the method is what Plato's given you.