LUNEX 5 (free electron Laser Using a New accelerator for the Exploitation of X-ray radiation of 5 th generation) aims at investigation the production of short intense and coherent pulses in the soft X-ray region with innovative schemes (such as echo and seeding with harmonics generated in gas) and compact design. The undulators of the FEL line are designed to provide high field short period devices: modulators are in-vacuum undulators with a period of 30 mm and 0.27 m long, radiators are in-vacuum undulators with a period of 15 mm and 3 m long with a cryogenic option, relying on SOLEIL development experience of NdFeB U20 hybrid in-vacuum undulators and 2 m long PrFeB U18 cryogenic undulator operated at 77 K installed on a long straight section of SOLEIL, and ESRF development experience of many in-vacuum undulator and 2 NdFeB U18 cryogenic undulators operating at 150 K. In addition, the line comports electromagnetic quadrupoles for the beam focusing, chicane dipoles for the beam compression and an electromagnetic bending magnet for the beam dump. A prototype of cryo-ready radiator is under design. Variable permanent magnet quadrupoles are under study for the transport of the Laser WakeField Accelerator towards the undulators.