The Korea Basic Science Institute (KBSI) has initiated the development of a 5 T high temperature superconductor (HTS) insert magnet system. The objective of the program is the design and fabrication of HTS insert magnet system for high field magnet applications. The primary requirement for the cryostat of the HTS insert magnet is to use the existing background magnet. The HTS magnet system therefore should be inserted into the conduction-cooled 15 T background magnet with 102 mm room-temperature bore. Consequently, several ancillary requirements such as space restriction and cryostat structure need technical attention. In this paper, the design of liquid helium cryostat for a 5 T HTS insert magnet is presented, taking into account cryogenic loads and inventory of cryogenic liquid. In addition, the structure of cryostat, minimizing unwanted heat flow from room-temperature to cryogenic-temperature, is described in detail. Based upon this design, the cryostat is fabricated and the performance of cryostat is discussed using the preliminary results of a cooling test.