Magnetic and magnetocaloric properties of single crystalline Er5Si4 have been investigated as a function of the applied magnetic field (up to 50 kOe) and the hydrostatic pressure (up to 10 kbar) in the 5-300 K temperature range along the three main crystallographic directions. The magnetization isotherms show a highly anisotropic behaviour with the easy-magnetization direction along the b-axis for the low-pressure monoclinic and high-pressure orthorhombic structures, in good agreement with previous neutron scattering experiments. Below T C the approach to the saturation shows a step-like behaviour when the magnetic field is applied along the hard directions. The steps are sharper as the pressure increases. At constant magnetic field change, increasing the pressure induces a highly anisotropic enhancement of the magnetic entropy change. An enhancement of 20 % is observed along the easy axis b, where the magnetic entropy change is maximum. The different evolution of the magnitude and temperature dependence of the magnetocaloric effect (MCE) along the three crystallographic directions with pressure is discussed.