\[\boxed{\mathbf{677}\mathbf{.}}\]
\[1)\ tg\left( \pi + arctg\frac{5}{4} \right) =\]
\[= \text{tg}\left( \text{arctg}\frac{5}{4} \right) = \frac{5}{4};\]
\[2)\ ctg\left( \frac{\pi}{2} - arctg\ 2 \right) =\]
\[= \text{tg\ }(arctg\ 2) = 2.\]