We report the discovery and subsequent multiwavelength afterglow behaviour of the high-redshift (z= 4.27) Gamma Ray Burst (GRB) 050505. This burst is the third most-distant burst, measured by spectroscopic redshift, discovered after GRB 000131 (z= 4.50) and GRB 050904 (z= 6.29). GRB 050505 is a long GRB with a multipeaked γ-ray light curve, with a duration of T90= 63 ± 2 s and an inferred isotropic release in γ-rays of ∼ 4.44 × 1053 erg in the 1–104 keV rest-frame energy range. The Swift X-Ray Telescope followed the afterglow for 14 d, detecting two breaks in the light curve at 7.4 +1.5−1.5 and 58.0 +9.9−15.4 ks after the burst trigger. The power-law decay slopes before, between and after these breaks were 0.25+0.16−0.17, 1.17+0.08−0.09 and 1.97+0.27−0.28, respectively. The light curve can also be fitted with a ‘smoothly broken’ power-law model with a break observed at ∼T+ 18.5 ks, with decay slopes of ∼0.4 and ∼1.8, before and after the break, respectively. The X-ray afterglow shows no spectral variation over the course of the Swift observations, being well fitted with a single power law of photon index ∼1.90. This behaviour is expected for the cessation of the continued energization of the interstellar medium shock, followed by a break caused by a jet, either uniform or structured. Neither break is consistent with a cooling break. The spectral energy distribution, indeed, shows the cooling frequency to be below the X-ray but above the optical frequencies. The optical–X-ray spectrum also shows that there is significant X-ray absorption in excess of that due to our Galaxy but very little optical–ultraviolet extinction, with E(B−V) ≈ 0.10 for a Small Magellanic Cloud like extinction curve.