如图， $△\mathit{ABC}$的边 $\mathit{AB}=30\text{cm},\mathit{AC}=25\text{cm}$，点 $D,F$在 $\mathit{AC}$上，点 $E,G$在 $\mathit{AB}$上， $S_{△\mathit{ADE}}:S_{△\mathit{DEF}}:S_{△\mathit{EFG}}:S_{△\mathit{FGC}}:S_{△\mathit{CBC}}=1:2:3:4:5$，求 $\mathit{AD}$和 $\mathit{GE}$的长．