5. Упростить выражения: 1) \((\overrightarrow{AB}+\overrightarrow{BC}-\overrightarrow{MC})+(\overrightarrow{MD}-\overrightarrow{KD})\); 2) \((\overrightarrow{CB}+\overrightarrow{AC}+\overrightarrow{BD})-(\overrightarrow{MK}+\overrightarrow{KD})\).

1)

\[\begin{aligned}\overrightarrow{AB}+\overrightarrow{BC}-\overrightarrow{MC}+\overrightarrow{MD}-\overrightarrow{KD}&=\overrightarrow{AC}+\overrightarrow{CM}+\overrightarrow{MK}\\&=\overrightarrow{AK}.\end{aligned}\]

Здесь \(-\overrightarrow{MC}=\overrightarrow{CM}\), а \(\overrightarrow{MD}-\overrightarrow{KD}=\overrightarrow{MD}+\overrightarrow{DK}=\overrightarrow{MK}\).

2)

\[\begin{aligned}\overrightarrow{CB}+\overrightarrow{AC}+\overrightarrow{BD}-\overrightarrow{MK}-\overrightarrow{KD}&=\overrightarrow{AB}+\overrightarrow{BD}-\overrightarrow{MD}\\&=\overrightarrow{AD}-\overrightarrow{MD}\\&=\overrightarrow{AD}+\overrightarrow{DM}=\overrightarrow{AM}.\end{aligned}\]

Ответ: 1) \(\overrightarrow{AK}\); 2) \(\overrightarrow{AM}\).