Calculate approximately the expression $A = 5^{1/2} \cdot 5^{1/4} \cdot 5^{1/8}\cdot\ldots$

My books says to says to do this:

$ 5^{1/4} \cdot 5^{1/8} \cdot 5^{1/16}\cdot\ldots = A $

Then

$ A = \sqrt {5A} \Longrightarrow A^2 = 5A \Longrightarrow A =5 $

Why $ 5^{1/4}\cdot 5^{1/8}\cdot 5^{1/16}\cdot\ldots = A $ ??

Thank you.