A function f is defined by the following.

f$($x$)=1+5$x $+$ x$2+5$x$3+$ x$4+$

That is$,$ its coefficients are

c$2$n $=1$

and

c$2$n $+1=5$

for all

n $0.$

Find the interval of convergence of the series. $($Enter your answer using interval notation.$)$