The values of a function $f(x)$ are given in the table below.
x 1 2 3 5 8 13
f(x) 3 13 8 1 0 5
If $f^{-1}$ exists, what is $f^{-1}\left(\frac{f^{-1}(5) +f^{-1}(13)}{f^{-1}(1)}\right)$?
\(f^{-1}\left(\frac{f^{-1}(5) +f^{-1}(13)}{f^{-1}(1)}\right) = \boxed{3}\)
