Magnetic and structural properties of single crystalline Gd5Si2Ge2 under hydrostatic pressure have been characterized by using magnetization, linear thermal expansion, and compressibility measurements. A strong dependence of Curie temperature on pressure, dT(C)/dP=+4.8 K/kbar, is observed in contrast with the smaller values of about 3 K/kbar found in polycrystalline specimens. This difference reflects the role the microstructure may play in pressure-induced magnetic-crystallographic phase changes, likely related to stress relaxation at the grain boundaries, domain pinning and/or nucleation of defects. The pressure dependence of the critical magnetic field, d(dH(C)/dT)/dP, drops at the rate -0.122(5)kOe/K kbar, which points to an enhancement of the magnetoelastic coupling with pressure. The latter affects the magnetocaloric behavior of the material at the rate d(Delta S-M)/dP congruent to 1.8 J/kg K kbar. The linear thermal expansion confirms the strongly anisotropic change of the lattice parameters through the orthorhombic to monoclinic crystallographic transformation with Delta a/a=+0.94%, Delta b/b=-0.13%, and Delta c/c=-0.22%. The structural transition temperature varies with pressure synchronously with the Curie temperature, and the size and shape of the strain anomalies remain nearly unaffected by the hydrostatic pressure, indicating, respectively, that the structural and magnetic transformations remain coupled, and the anisotropic behavior of the lattice is preserved as pressure increases. The room temperature linear compressibility data show that the magnetostructural transformation can be triggered isothermally at similar to 6 kbar and that the compressibility is anisotropic.