The Xiao conjecture predicts that the relative irregularity q_f:=q(S)-g(B) of a fibered surface f: S--->B is at most g/2+1, where g is the genus of the general fiber. It was proven by Barja, González-Alonso, and Naranjo when the general fiber has maximal Clifford index. I will present a proof of the Xiao conjecture for surfaces fibered by trigonal genus 5 curves, which completes the proof of the Xiao conjecture for surfaces fibered by genus 5 curves.