To factor $ st+5s-2t-10 $ we can use factoring by grouping.
Group $ \color{blue}{ st }$ with $ \color{blue}{ 5s }$ and $ \color{red}{ -2t }$ with $ \color{red}{ -10 }$ then factor each group.
$$ \begin{aligned} st+5s-2t-10 &= ( \color{blue}{ st+5s } ) + ( \color{red}{ -2t-10 }) = \\ &= \color{blue}{ s( t+5 )} \color{red}{ -2( t+5 ) } = \\ &= (s-2)(t+5) \end{aligned} $$