This paper presents the design, fabrication, and test results of the first 5 T wavelength shifter (WLS) magnet with high-temperature superconductor (HTS) incorporated. Key questions of the study are the applicability of HTS magnet to the accelerator system, and problems regarding these questions are the manufacturability of HTS accelerator magnet and the effect of screening current induced field during HTS magnet operation. Key challenges are the (1) Lorentz force-induced high mechanical stress, (2) undefined design and manufacturing methods of HTS accelerator magnet, and (3) 3D screening current-induced field analysis model with nonlinear iron characteristics considered. To solve the difficulties of HTS magnet protection and the high operation cost of liquid helium cooling, we suggested conduction-cooled liquid helium-free metal insulated (MI) HTS WLS magnet for accelerator-based light source. First, we performed the electromagnetic design of the WLS magnet considering the field requirement as well as the critical current property of the HTS conductor.