Sc5Rh6Sn18 with a cage-type quasiskutterudite crystal lattice and type II superconductivity, with superconducting transition temperature Tc = 4.99 K, was investigated under hydrostatic high-pressure (HP) using electrical transport, synchrotron X-ray diffraction (XRD) and Raman spectroscopy. Our data show that HP enhance the metallic nature and Tc of the system. Tc is found to show a continuous increase reaching to 5.24 K at 2.5 GPa. Athough the system is metallic in nature, Raman spectroscopy investigations at ambient pressure revealed the presence of three weak modes at 165.97, 219.86 and 230.35 cm-1, mostly related to the rattling atom Sc. The HP-XRD data revealed that the cage structure was stable without any structural phase transition up to ~7 GPa. The lattice parameters and volume exhibited a smooth decrease without any anomalies as a function of pressure in this pressure range. In particular, a second order Birch-Murnaghan equation of state can describe the pressure dependence of the unit cell volume well, yielding a bulk modulus of ~ 97 GPa. HP Raman investigations revealed a linear shift of all the three Raman modes to higher wavenumbers with increasing pressure up to ~8 GPa. As the pressure enhances the bond overlap, thus inducing more electronic charges into the system, HP-XRD and Raman results may indciate the possibility of obtaining higher Tc with increasing pressures in this pressure range.