$($a$)$ Give the domain of the function $y=x^{\frac{4}{5}}.($Enter your answer using interval notation.$)$

$($b$)$ Give the largest interval I of definition over which $y=x^{\frac{4}{5}}$ is a solution of the differential equation $5x{y}^{\text{'}}-4y=0.($Enter your answer using interval notation.$)(-,)$