Finding power series for given values of a sum

I have this exercise which I'm not sure how to solve.

It says: Consider the series $\displaystyle \displaystyle\sum_{n=0}^{\infty}x^n$ Does exists any value of x for which the series converges to five? ¿and to 1/3?

Well, I've reasoned that if there exists that value, then it must be inside of the radius of convergence for the series. So I've found the radius of convergence:

$\displaystyle a_n=1$

$\displaystyle R=\displaystyle\lim_{n \to{}\infty}{\left |{\displaystyle\frac{a_n}{a_{n+1}}}\right |}=1$

But now I don't know how to proceed.