jmc

We could evaluate directly: $$\begin{array}{rl}[a-(b-c)]-[(a-b)-c]& =[17-(21-5)]-[(17-21)-5]\\ & =[17-16]-[-4-5]\\ & =1-(-9)=\boxed{10}.\end{array}$$

We also could have simplified the expression first: $$\begin{array}{rl}[a-(b-c)]-[(a-b)-c]& =[a-b+c]-[a-b-c]\\ & =a-b+c-a+b+c\\ & =2c.\end{array}$$ Then, we have $2c=2(5)=10$.