We can use the properties of logarithms to simplify this expression. Recall that \(\log_{a} b^{c} = c\log_{a} b\) and \(\log_{a} \sqrt{b} = \frac{1}{2}\log_{a} b\).
So, \[\frac{\log_{5} 8}{\log_{5} \sqrt{8}} = \frac{\log_{5} 8}{\frac{1}{2}\log_{5} 8} = \frac{2\log_{5} 8}{\log_{5} 8} = \boxed{2}.\]
Therefore, the answer is 2.