The reionisation of the Universe is a process that is thought to have ended around z~6, as inferred from spectroscopy of distant bright background sources, such as quasars (QSO) and gamma-ray burst (GRB) afterglows. Furthermore, spectroscopy of a GRB afterglow provides insight in its host galaxy, which is often too dim and distant to study otherwise. For the Swift GRB 130606A at z=5.913 we have obtained a high S/N spectrum covering the full optical and near-IR wavelength region at intermediate spectral resolution with VLT/X-Shooter. We aim to measure the degree of ionisation of the intergalactic medium (IGM) between z=5.02-5.84 and to study the chemical abundance pattern and dust content of its host galaxy. We estimated the UV continuum of the GRB afterglow using a power-law extrapolation, then measured the flux decrement due to absorption at Ly{alpha},{beta}, and {gamma} wavelength regions. Furthermore, we fitted the shape of the red damping wing of Ly{alpha}. The hydrogen and metal absorption lines formed in the host galaxy were fitted with Voigt profiles to obtain column densities. We investigated whether ionisation corrections needed to be applied.