Error in my proof? What is wrong in this proof. It seems correct to me but still doesn't make proper sense.
$$\sqrt{\cdots\sqrt{\sqrt{\sqrt{5}}}}=5^{1/\infty}=5^0=1$$
EDIT
So does this mean that
$5^{1/\infty} = 1$
$(5^{1/\infty})^\infty = 1^\infty$
But according to me, $1^\infty$ is indeterminate.

Note that $\lim_{n\to \infty}x_n^{y_n}=(\lim_{n\to \infty}x_n)^{\lim_{n\to \infty}y_n}$
