\[4\frac{5^{\backslash 5}}{6} + 3\frac{3^{\backslash 3}}{10} = 4\frac{25}{30} + 3\frac{9}{30} =\]
\[= 7 + \frac{32}{30} = 7 + 1\frac{2}{30} =\]
\[= 7 + 1\frac{1}{15} = 8\frac{1}{15}.\]