Classify the following numbers as rational or irrational with justification:
$(i)$ $0.5918$
$(ii)$ $(1+\sqrt{5})-(4+\sqrt{5})$

(N/A) $(i)$ $0.5918$ is a terminating decimal expansion. Any number that can be expressed as a terminating decimal is a rational number because it can be written in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$. Here,$0.5918 = \frac{5918}{10000}$,which is rational.
$(ii)$ Simplify the expression: $(1+\sqrt{5})-(4+\sqrt{5}) = 1 + \sqrt{5} - 4 - \sqrt{5} = 1 - 4 = -3$. Since $-3$ can be written as $\frac{-3}{1}$,which is in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$,it is a rational number.