\[2\frac{3^{\backslash 5}}{4} + 3\frac{2^{\backslash 4}}{5} = 2\frac{3 \cdot 5}{20} + 3\frac{2 \cdot 4}{20} =\]
\[= 2\frac{15}{20} + 3\frac{8}{20} = 5\frac{23}{20} = 6\frac{3}{20}.\]