a.
TH1 : x<1
\(\Rightarrow-x+1+3-x=5\\ \Rightarrow-2x+4=5\\ \Rightarrow-2x=1\\ \Rightarrow x=-\dfrac{1}{2}\left(tm\right)\)
TH2: \(1\le x< 3\)
\(\Rightarrow x-1+3-x=5\\ \Rightarrow0x=3\\ \Rightarrow x\in\varnothing\)
TH3: \(x\ge3\)
\(\Rightarrow x-1+x-3=5\\ \Rightarrow2x-4=5\\ \Rightarrow2x=9\\ \Rightarrow x=\dfrac{9}{2}\left(tm\right)\)