Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of Tb5Si2Ge2 have been studied by means of macroscopic (thermal expansion and magnetization) and microscopic (neutron powder diffraction) techniques. We present evidence that the high-temperature second-order ferromagnetic transition can be coupled with the low-temperature first-order structural phase change into a single first-order magnetic-crystallographic transformation at and above a tricritical point in the vicinity of 8.6 kbar. This pressure-induced coupling has a remarkable effect on the magnetocaloric effect, transforming Tb5Si2Ge2 from an ordinary into a giant magnetocaloric effect material.